About this topic
Summary Category theory is a branch of mathematics that has played a very important role in twentieth and twenty-first century mathematics. A category is a mathematical structure made up of objects (which can be helpfully thought of as mathematical structures of some sort) and morphisms (which can helpfully be thought of as abstract mappings connecting the objects). A canonical example of a category is the category with sets for objects and functions for morphisms. From the philosophical perspective category theory is important for a variety of reasons, including its role as an alternative foundation for mathematics, because of the development and growth of categorial logic, and for its role in providing a canonical codification of the notion of isomorphism.
Key works The definitions of categories, functors, and natural transformations all appeared for the first time in MacLane & Eilenberg 1945. This paper is difficult for a variety of both historical and mathematical reasons; the standard textbook on category theory is Maclane 1978. Textbooks aimed more at philosophical audiences include Goldblatt 2006, Awodey 2010, and McLarty 1995. For discussion on the role of category theory as an autonomous foundation of mathematics, the conversation contained in the following papers is helpful: Feferman 1977, Hellman 2003, Awodey 2004, Linnebo & Pettigrew 2011, and Logan 2015. The references in these papers will direct the reader in helpful directions for further research.
Introductions Landry & Marquis 2005 and Landry 1999 provide excellent overviews of the area. Mclarty 1990 provides an overview of the history of philosophical uses of category theory focused on Topos theory. 
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Siblings:History/traditions: Category Theory

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  1. added 2020-06-16
    Jonahan Chapman and Frederick Rowbottom. Relative Category Theory and Geometric Morphisms. A Logical Approach. Oxford Logic Guides, No. 16., Clarendon Press, Oxford University Press, Oxford and New York1992, Xi + 263 Pp. [REVIEW]I. Moerdijk - 1995 - Journal of Symbolic Logic 60 (2):694-695.
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  2. added 2020-05-25
    Modes of Adjointness.C. Smith & M. Menni - 2014 - Journal of Philosophical Logic 43 (2-3):365-391.
    The fact that many modal operators are part of an adjunction is probably folklore since the discovery of adjunctions. On the other hand, the natural idea of a minimal propositional calculus extended with a pair of adjoint operators seems to have been formulated only very recently. This recent research, mainly motivated by applications in computer science, concentrates on technical issues related to the calculi and not on the significance of adjunctions in modal logic. It then seems a worthy enterprise to (...)
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  3. added 2020-02-10
    Yale Gallery Talk, Language Perception and Representation.PhD Tanya Kelley - forthcoming
    Yale Gallery Talk, Language Perception and Representation Tanya Kelley and James Prosek Linguist and artist Tanya Kelley, Ph.D., and artist, writer, and naturalist James Prosek, B.A. 1997, discuss color manuals used by artist-naturalists and biologists and lead visitors in close looking and drawing. Presented in conjunction with the exhibition James Prosek: Art, Artifact, Artifice. Space is limited. Open to: General Public .
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  4. added 2019-09-22
    The Logic in Philosophy of Science.Hans Halvorson - 2019 - Cambridge University Press.
    Major figures of twentieth-century philosophy were enthralled by the revolution in formal logic, and many of their arguments are based on novel mathematical discoveries. Hilary Putnam claimed that the Löwenheim-Skølem theorem refutes the existence of an objective, observer-independent world; Bas van Fraassen claimed that arguments against empiricism in philosophy of science are ineffective against a semantic approach to scientific theories; W. V. O. Quine claimed that the distinction between analytic and synthetic truths is trivialized by the fact that any theory (...)
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  5. added 2019-07-04
    Choice-Free Stone Duality.Nick Bezhanishvili & Wesley H. Holliday - 2020 - Journal of Symbolic Logic 85 (1):109-148.
    The standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean (...)
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  6. added 2019-06-07
    Thomas Pratsch, Der hagiographische Topos. Griechische Heiligenviten in mittelbyzantinischer Zeit.Stephanos Efthymiadis - 2008 - Byzantinische Zeitschrift 100 (1):249-252.
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  7. added 2019-06-06
    The Logic of Partitions: Introduction to the Dual of the Logic of Subsets: The Logic of Partitions.David Ellerman - 2010 - Review of Symbolic Logic 3 (2):287-350.
    Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as the logic of subsets of (...)
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  8. added 2019-06-06
    A Note On The Axiomatisation Of Real Numbers.Thierry Coquand & L. Henri Lombardi - 2008 - Mathematical Logic Quarterly 54 (3):224-228.
    Is it possible to give an abstract characterisation of constructive real numbers? A condition should be that all axioms are valid for Dedekind reals in any topos, or for constructive reals in Bishop mathematics. We present here a possible first-order axiomatisation of real numbers, which becomes complete if one adds the law of excluded middle. As an application of the forcing relation defined in [3, 2], we give a proof that the formula which specifies the maximum function is not provable (...)
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  9. added 2019-06-06
    On the Validity of Hilbert's Nullstellensatz, Artin's Theorem, and Related Results in Grothendieck Toposes.W. A. MacCaull - 1988 - Journal of Symbolic Logic 53 (4):1177-1187.
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  10. added 2019-06-06
    Functional Completeness of Cartesian Categories.J. Lambek - 1974 - Annals of Pure and Applied Logic 6 (3):259.
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  11. added 2019-06-03
    Canonical Maps.Jean-Pierre Marquis - 2018 - In Elaine Landry (ed.), Categories for the Working Philosophers. Oxford, UK: pp. 90-112.
    Categorical foundations and set-theoretical foundations are sometimes presented as alternative foundational schemes. So far, the literature has mostly focused on the weaknesses of the categorical foundations. We want here to concentrate on what we take to be one of its strengths: the explicit identification of so-called canonical maps and their role in mathematics. Canonical maps play a central role in contemporary mathematics and although some are easily defined by set-theoretical tools, they all appear systematically in a categorical framework. The key (...)
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  12. added 2019-05-30
    The Cell and Protoplasm as Container, Object, and Substance, 1835–1861.Daniel Liu - 2017 - Journal of the History of Biology 50 (4):889-925.
    (Recipient of the 2020 Everett Mendelsohn Prize.) This article revisits the development of the protoplasm concept as it originally arose from critiques of the cell theory, and examines how the term “protoplasm” transformed from a botanical term of art in the 1840s to the so-called “living substance” and “the physical basis of life” two decades later. I show that there were two major shifts in biological materialism that needed to occur before protoplasm theory could be elevated to have equal status (...)
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  13. added 2019-05-15
    Saunders Mac Lane and Ieke Moerdijk. Sheaves in Geometry and Logic. A First Introduction to Topos Theory. Universitext. Springer-Verlag, New York, Berlin, Etc., 1992, Xii – 627 Pp. [REVIEW]Andrew M. Pitts - 1995 - Journal of Symbolic Logic 60 (1):340-342.
  14. added 2019-05-14
    Andrew M. Pitts. Interpolation and Conceptual Completeness for Pretoposes Via Category Theory. Mathematical Logic and Theoretical Computer Science, Edited by Kueker David W., Lopez-Escobar Edgar G. K. And Smith Carl H., Lecture Notes in Pure and Applied Mathematics, Vol. 106, Marcel Dekker, New York and Basel1987, Pp. 301–327. - Andrew M. Pitts. Conceptual Completeness for First-Order Intuitionistic Logic: An Application of Categorical Logic. Annals of Pure and Applied Logic, Vol. 41 , Pp. 33–81. [REVIEW]Marek Zawadowski - 1995 - Journal of Symbolic Logic 60 (2):692-694.
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  15. added 2019-05-06
    Peter T. Johnstone. Sketches of an Elephant: A Topos Theory Compendium. Oxford Logic Guides, Vols. 43, 44. Oxford University Press, Oxford, 2002, Xxii + 1160 Pp. [REVIEW]Steve Awodey - 2005 - Bulletin of Symbolic Logic 11 (1):65-69.
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  16. added 2019-01-28
    On the Notion of Truth in Quantum Mechanics: A Category-Theoretic Standpoint.Vassilios Karakostas & Elias Zafiris - 2016 - In Diederik Aerts, Christian de Ronde, Hector Freytes & Roberto Giuntini (eds.), Probing the Meaning and Structure of Quantum Mechanics: Semantics, Dynamics and Identity. World Scientific. pp. 1-43.
    The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valua- tion in quantum mechanics as exemplified, in particular, by Kochen-Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event al- gebras. We show explicitly that the latter category is equipped with an object of (...)
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  17. added 2019-01-28
    Rosen's Modelling Relations Via Categorical Adjunctions.Elias Zafiris - 2012 - International Journal of General Systems 41 (5):439-474.
    Rosen's modelling relations constitute a conceptual schema for the understanding of the bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems used in this study refers to information structures constructed as algebraic rings of observable attributes of natural systems, in which the notion of observable signifies a physical attribute that, in principle, can be measured. Due to the fact that modelling relations are bidirectional by construction, they admit a precise categorical formulation in terms (...)
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  18. added 2019-01-28
    Boolean Information Sieves: A Local-to-Global Approach to Quantum Information.Elias Zafiris - 2010 - International Journal of General Systems 39 (8):873-895.
    We propose a sheaf-theoretic framework for the representation of a quantum observable structure in terms of Boolean information sieves. The algebraic representation of a quantum observable structure in the relational local terms of sheaf theory effectuates a semantic transition from the axiomatic set-theoretic context of orthocomplemented partially ordered sets, la Birkhoff and Von Neumann, to the categorical topos-theoretic context of Boolean information sieves, la Grothendieck. The representation schema is based on the existence of a categorical adjunction, which is used as (...)
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  19. added 2019-01-28
    Categorical Modeling of Natural Complex Systems. Part II: Functorial Process of Localization-Globalization.Elias Zafiris - 2008 - Advances in Systems Science and Applications 8 (3):367-387.
    We develop a general covariant categorical modeling theory of natural systems' behavior based on the fundamental functorial processes of representation and localization-globalization. In the second part of this study we analyze the semantic bidirectional process of localization-globalization. The notion of a localization system of a complex information structure bears a dual role: Firstly, it determines the appropriate categorical environment of base reference contexts for considering the operational modeling of a complex system's behavior, and secondly, it specifies the global compatibility conditions (...)
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  20. added 2019-01-28
    Categorical Modeling of Natural Complex Systems. Part I: Functorial Process of Representation.Elias Zafiris - 2008 - Advances in Systems Science and Applications 8 (2):187-200.
    We develop a general covariant categorical modeling theory of natural systems’ behavior based on the fundamental functorial processes of representation and localization-globalization. In the first part of this study we analyze the process of representation. Representation constitutes a categorical modeling relation that signifies the semantic bidirectional process of correspondence between natural systems and formal symbolic systems. The notion of formal systems is substantiated by algebraic rings of observable attributes of natural systems. In this perspective, the distinction between simple and complex (...)
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  21. added 2019-01-28
    Quantum Observables Algebras and Abstract Differential Geometry: The Topos-Theoretic Dynamics of Diagrams of Commutative Algebraic Localizations.Elias Zafiris - 2007 - International Journal of Theoretical Physics 46 (2):319-382.
    We construct a sheaf-theoretic representation of quantum observables algebras over a base category equipped with a Grothendieck topology, consisting of epimorphic families of commutative observables algebras, playing the role of local arithmetics in measurement situations. This construction makes possible the adaptation of the methodology of Abstract Differential Geometry (ADG), à la Mallios, in a topos-theoretic environment, and hence, the extension of the “mechanism of differentials” in the quantum regime. The process of gluing information, within diagrams of commutative algebraic localizations, generates (...)
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  22. added 2019-01-28
    Category-Theoretic Analysis of the Notion of Complementarity for Quantum Systems.Elias Zafiris - 2006 - International Journal of General Systems 35 (1):69-89.
    In this paper we adopt a category-theoretic viewpoint in order to analyze the semantics of complementarity for quantum systems. Based on the existence of a pair of adjoint functors between the topos of presheaves of the Boolean kind of structure and the category of the quantum kind of structure, we establish a twofold complementarity scheme which constitutes an instance of the concept of adjunction. It is further argued that the established scheme is inextricably connected with a realistic philosophical attitude, although (...)
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  23. added 2019-01-28
    Generalized Topological Covering Systems on Quantum Events' Structures.Elias Zafiris - 2006 - Journal of Physics A: Mathematics and Applications 39 (6):1485-1505.
    Homologous operational localization processes are effectuated in terms of generalized topological covering systems on structures of physical events. We study localization systems of quantum events' structures by means of Gtothendieck topologies on the base category of Boolean events' algebras. We show that a quantum events algebra is represented by means of a Grothendieck sheaf-theoretic fibred structure, with respect to the global partial order of quantum events' fibres over the base category of local Boolean frames.
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  24. added 2019-01-28
    Sheaf-Theoretic Representation of Quantum Measure Algebras.Elias Zafiris - 2006 - Journal of Mathematical Physics 47 (9).
    We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras. The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet axiomatization at the level of (...)
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  25. added 2019-01-28
    Interpreting Observables in a Quantum World From the Categorial Standpoint.Elias Zafiris - 2004 - International Journal of Theoretical Physics 43 (1):265-298.
    We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and (...)
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  26. added 2019-01-27
    Boolean Localization Of Quantum Events: A Processual Sheaf-Theoretic Approach.Elias Zafiris - 2016 - In David Ray Griffin, Michael Epperson & Timothy E. Eastman (eds.), Physics and Speculative Philosophy: Potentiality in Modern Science. De Gruyter. pp. 107-126.
  27. added 2019-01-27
    Differential Sheaves and Connections: A Natural Approach to Physical Geometry.Anastasios Mallios & Elias Zafiris - 2015 - World Scientific.
    This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to "physical geometry". In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory (...)
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  28. added 2018-03-26
    Iconicity and Abduction.Rocco Gangle & Gianluca Caterina - 2016 - New York, USA: Springer.
  29. added 2018-02-17
    Complex Non-Linear Biodynamics in Categories, Higher Dimensional Algebra and ŁUkasiewicz''“Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks.I. C. Baianu, R. Brown, G. Georgescu & J. F. Glazebrook - 2006 - Axiomathes 16 (1):65-122.
    A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil (...)
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  30. added 2017-12-14
    Linear Structures, Causal Sets and Topology.Hudetz Laurenz - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B):294-308.
    Causal set theory and the theory of linear structures share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. I show that causal set theory can be embedded into Maudlin’s more general framework and I characterise what Maudlin’s topological concepts boil down to when applied to discrete linear structures that correspond to causal sets. Moreover, I show that all topological aspects of (...)
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  31. added 2017-12-04
    Axiomatizing Category Theory in Free Logic.Christoph Benzmüller & Dana Scott - manuscript
    Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL interactive proof assistant, and this formalization utilizes a semantically correct embedding of free logic in classical higher-order logic. The modeling and formal analysis of our axiom sets has been significantly supported by series of experiments with automated reasoning tools integrated with Isabelle/HOL. We also address the (...)
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  32. added 2017-12-04
    Grothendieck Universes and Indefinite Extensibility.Hasen Khudairi - manuscript
    This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility in the category-theoretic setting is identifiable with the Kripke functors of modal coalgebraic automata, where the automata model Grothendieck Universes and the functors are further inter-definable with the elementary embeddings of large cardinal axioms. The Kripke functors definable in Grothendieck universes are argued to account for the ontological expansion effected by the elementary embeddings in the (...)
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  33. added 2017-12-04
    Approximating Cartesian Closed Categories in NF-Style Set Theories.Morgan Thomas - 2018 - Journal of Philosophical Logic 47 (1):143-160.
    I criticize, but uphold the conclusion of, an argument by McLarty to the effect that New Foundations style set theories don’t form a suitable foundation for category theory. McLarty’s argument is from the fact that Set and Cat are not Cartesian closed in NF-style set theories. I point out that these categories do still have a property approximating Cartesian closure, making McLarty’s argument not conclusive. After considering and attempting to address other problems with developing category theory in NF-style set theories, (...)
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  34. added 2017-12-04
    Concrete Fibrations.Ruggero Pagnan - 2017 - Notre Dame Journal of Formal Logic 58 (2):179-204.
    As far as we know, no notion of concrete fibration is available. We provide one such notion in adherence to the foundational attitude that characterizes the adoption of the fibrational perspective in approaching fundamental subjects in category theory and discuss it in connection with the notion of concrete category and the notions of locally small and small fibrations. We also discuss the appropriateness of our notion of concrete fibration for fibrations of small maps, which is relevant to algebraic set theory.
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  35. added 2017-12-04
    A Brief Introduction to Transcendental Phenomenology and Conceptual Mathematics.Nicholas Lawrence - 2017 - Dissertation,
    By extending Husserl’s own historico-critical study to include the conceptual mathematics of more contemporary times – specifically category theory and its emphatic development since the second half of the 20th century – this paper claims that the delineation between mathematics and philosophy must be completely revisited. It will be contended that Husserl’s phenomenological work was very much influenced by the discoveries and limitations of the formal mathematics being developed at Göttingen during his tenure there and that, subsequently, the rôle he (...)
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  36. added 2017-12-04
    Categorical Harmony and Path Induction.Patrick Walsh - 2017 - Review of Symbolic Logic 10 (2):301-321.
    This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent conceptions of harmony through category theory. (...)
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  37. added 2017-12-04
    Category Theory and Set Theory as Theories About Complementary Types of Universals.David P. Ellerman - 2017 - Logic and Logical Philosophy 26 (2):1-18.
    Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal u_{F}={x|F(x)} for a property F() could never be self-predicative in the sense of u_{F}∈u_{F}. But the mathematical theory of categories, (...)
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  38. added 2017-12-04
    Mathematical Frameworks for Consciousness.Menas Kafatos & Narasimhan - 2016 - Cosmos and History 12 (2):150-159.
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  39. added 2017-12-04
    Brain Functors: A Mathematical Model for Intentional Perception and Action.David Ellerman - 2016 - Brain: Broad Research in Artificial Intelligence and Neuroscience 7 (1):5-17.
    Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it is split into two parts, a left and a right semiadjunction. Semiadjunctions (...)
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  40. added 2017-12-04
    On a Paraconsistentization Functor in the Category of Consequence Structures.Edelcio G. De Souza, Alexandre Costa-Leite & Diogo H. B. Dias - 2016 - Journal of Applied Non-Classical Logics 26 (3):240-250.
    This paper is an attempt to solve the following problem: given a logic, how to turn it into a paraconsistent one? In other words, given a logic in which ex falso quodlibet holds, how to convert it into a logic not satisfying this principle? We use a framework provided by category theory in order to define a category of consequence structures. Then, we propose a functor to transform a logic not able to deal with contradictions into a paraconsistent one. Moreover, (...)
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  41. added 2017-12-04
    Does Homotopy Type Theory Provide a Foundation for Mathematics?James Ladyman & Stuart Presnell - 2016 - British Journal for the Philosophy of Science:axw006.
    Homotopy Type Theory is a putative new foundation for mathematics grounded in constructive intensional type theory that offers an alternative to the foundations provided by ZFC set theory and category theory. This article explains and motivates an account of how to define, justify, and think about HoTT in a way that is self-contained, and argues that, so construed, it is a candidate for being an autonomous foundation for mathematics. We first consider various questions that a foundation for mathematics might be (...)
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  42. added 2017-12-04
    Neat Embeddings as Adjoint Situations.Tarek Sayed-Ahmed - 2015 - Synthese 192 (7):1-37.
    Looking at the operation of forming neat $\alpha $ -reducts as a functor, with $\alpha $ an infinite ordinal, we investigate when such a functor obtained by truncating $\omega $ dimensions, has a right adjoint. We show that the neat reduct functor for representable cylindric algebras does not have a right adjoint, while that of polyadic algebras is an equivalence. We relate this categorial result to several amalgamation properties for classes of representable algebras. We show that the variety of cylindric (...)
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  43. added 2017-12-04
    Relational Realism: A New Foundation for Quantum Mechanics?: Michael Epperson and Elias Zafiris: Foundations of Relational Realism: A Topological Approach to Quantum Mechanics and the Philosophy of Nature. Lanham, Maryland: Lexington Books, 2013, Xviii+419pp, $101.28 HB.Nicholas J. Teh - 2015 - Metascience 24 (2):205-209.
    Foundations of Relational Realism: A Topological Approach to Quantum Mechanics and the Philosophy of Nature by Michael Epperson and Elias Zafiris sets out to achieve three goals: to develop a version of Whiteheadian metaphysics that the authors call “relational realism”; to formalize relational realism in terms of category theory, in particular sheaf theory; and to use relational realism to solve the interpretative problems of quantum mechanics. These goals are ambitious, to say the least, and all this is leaving aside those (...)
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  44. added 2017-12-04
    Category Theory, Logic and Formal Linguistics: Some Connections, Old and New.Jean Gillibert & Christian Retoré - 2014 - Journal of Applied Logic 12 (1):1-13.
  45. added 2017-12-04
    The Categorical Imperative: Category Theory as a Foundation for Deontic Logic.Clayton Peterson - 2014 - Journal of Applied Logic 12 (4):417-461.
  46. added 2017-12-04
    The Minimal Levels of Abstraction in the History of Modern Computing.Federico Gobbo & Marco Benini - 2014 - Philosophy and Technology 27 (3):327-343.
    From the advent of general purpose, Turing-complete machines, the relation between operators, programmers and users with computers can be observed as interconnected informational organisms (inforgs), henceforth analysed with the method of levels of abstraction (LoAs), risen within the philosophy of information (PI). In this paper, the epistemological levellism proposed by L. Floridi in the PI to deal with LoAs will be formalised in constructive terms using category theory, so that information itself is treated as structure-preserving functions instead of Cartesian products. (...)
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  47. added 2017-12-04
    The Genetic Versus the Axiomatic Method: Responding to Feferman 1977: The Genetic Versus the Axiomatic Method: Responding to Feferman 1977.Elaine Landry - 2013 - Review of Symbolic Logic 6 (1):24-51.
    Feferman argues that category theory cannot stand on its own as a structuralist foundation for mathematics: he claims that, because the notions of operation and collection are both epistemically and logically prior, we require a background theory of operations and collections. Recently [2011], I have argued that in rationally reconstructing Hilbert’s organizational use of the axiomatic method, we can construct an algebraic version of category-theoretic structuralism. That is, in reply to Shapiro, we can be structuralists all the way down ; (...)
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  48. added 2017-12-04
    Foundations of Unlimited Category Theory: What Remains to Be Done: Foundations of Unlimited Category Theory: What Remains to Be Done.Solomon Feferman - 2013 - Review of Symbolic Logic 6 (1):6-15.
    Following a discussion of various forms of set-theoretical foundations of category theory and the controversial question of whether category theory does or can provide an autonomous foundation of mathematics, this article concentrates on the question whether there is a foundation for “unlimited” or “naive” category theory. The author proposed four criteria for such some years ago. The article describes how much had previously been accomplished on one approach to meeting those criteria, then takes care of one important obstacle that had (...)
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  49. added 2017-12-04
    The Methodological Roles of Tolerance and Conventionalism in the Philosophy of Mathematics: Reconsidering Carnap's Logic of Science.P. Doyle Emerson - unknown
    This dissertation makes two primary contributions. The first three chapters develop an interpretation of Carnap's Meta-Philosophical Program which places stress upon his methodological analysis of the sciences over and above the Principle of Tolerance. Most importantly, I suggest, is that Carnap sees philosophy as contiguous with science—as a part of the scientific enterprise—so utilizing the very same methods and subject to the same limitations. I argue that the methodological reforms he suggests for philosophy amount to philosophy as the explication of (...)
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  50. added 2017-12-04
    Anti-Foundational Categorical Structuralism.McDonald Darren - unknown
    The aim of this dissertation is to outline and defend the view here dubbed “anti-foundational categorical structuralism”. The program put forth is intended to provide an answer the question “what is mathematics?”. The answer here on offer adopts the structuralist view of mathematics, in that mathematics is taken to be “the science of structure” expressed in the language of category theory, which is argued to accurately capture the notion of a “structural property”. In characterizing mathematical theorems as both conditional and (...)
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