Understanding the infinite II: Coalgebra

In this paper we give an account of the rise and development of coalgebraic thinking in mathematics and computer science as an illustration of the way mathematical frameworks may be transformed. Originating in a foundational dispute as to the correct way to characterise sets, logicians and computer scientists came to see maximizing and minimizing extremal axiomatisations as a dual pair, each necessary to represent entities of interest. In particular, many important infinitely large entities can be characterised in terms of such axiomatisations. We consider reasons for the delay in arriving at the coalgebraic framework, despite many unrecognised manifestations occurring years earlier, and discuss an apparent asymmetry in the relationship between algebra and coalgebra
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DOI 10.1016/j.shpsa.2011.09.013
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References found in this work BETA
Quantum Quandaries: A Category-Theoretic Perspective.J. C. Baez - 2006 - In Dean Rickles, Steven French & Juha T. Saatsi (eds.), The Structural Foundations of Quantum Gravity. Clarendon Press.
A Brief Introduction to Algebraic Set Theory.Steve Awodey - 2008 - Bulletin of Symbolic Logic 14 (3):281-298.
A Restoration That Failed: Paul Finsler's Theory of Sets.Herbert Breger - 1992 - In Donald Gillies (ed.), Revolutions in Mathematics. Oxford University Press. pp. 249--264.
Non-Well-Founded Sets.Peter Aczel - 1988 - Csli Lecture Notes.

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Duality as a Category-Theoretic Concept.David Corfield - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59:55-61.

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