David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 56 (4):1243-1260 (1991)
Elementary axioms describe a category of categories. Theorems of category theory follow, including some on adjunctions and triples. A new result is that associativity of composition in categories follows from cartesian closedness of the category of categories. The axioms plus an axiom of infinity are consistent iff the axioms for a well-pointed topos with separation axiom and natural numbers are. The theory is not finitely axiomatizable. Each axiom is independent of the others. Further independence and definability results are proved. Relations between categories and sets, the latter defined as discrete categories, are described, and applications to foundations are discussed
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Michael Ernst (2015). The Prospects of Unlimited Category Theory: Doing What Remains to Be Done. Review of Symbolic Logic 8 (2):306-327.
Solomon Feferman (2013). Foundations of Unlimited Category Theory: What Remains to Be Done. Review of Symbolic Logic 6 (1):6-15.
Shay Allen Logan (forthcoming). Abstractionist Categories of Categories. Review of Symbolic Logic:1-17.
Elaine Landry (2011). How to Be a Structuralist All the Way Down. Synthese 179 (3):435 - 454.
Julian C. Cole (2010). Mathematical Structuralism Today. Philosophy Compass 5 (8):689-699.
Similar books and articles
Sidney R. Lehky (2005). Not All Categories Work the Same Way. Behavioral and Brain Sciences 28 (4):503-503.
Sven Ove Hansson (2006). Category-Specified Value Statements. Synthese 148 (2):425 - 432.
Takashi Ikegami (2005). Dynamical Categories and Language. Behavioral and Brain Sciences 28 (4):500-501.
Jan Westerhoff (2005). Ontological Categories: Their Nature and Significance. Oxford University Press.
Zoran Petrić (2002). Coherence in Substructural Categories. Studia Logica 70 (2):271 - 296.
Eleanor Rosch & Carolyn B. Mervis (1975). Family Resemblances: Studies in the Internal Structure of Categories. Cognitive Psychology 7 (4):573--605.
Evan Heit & Stephen P. Nicholson (2010). The Opposite of Republican: Polarization and Political Categorization. Cognitive Science 34 (8):1503-1516.
Jan Westerhoff (2004). The Construction of Ontological Categories. Australasian Journal of Philosophy 82 (4):595 – 620.
Added to index2009-01-28
Total downloads36 ( #89,896 of 1,725,418 )
Recent downloads (6 months)4 ( #167,246 of 1,725,418 )
How can I increase my downloads?