Foundations of Unlimited Category Theory: What Remains to Be Done

Review of Symbolic Logic 6 (1):6-15 (2013)
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Abstract

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 been met in that approach, and finally explains what remains to be done if one is to have a fully satisfactory solution.

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References found in this work

Category theory as an autonomous foundation.Øystein Linnebo & Richard Pettigrew - 2011 - Philosophia Mathematica 19 (3):227-254.
Axiomatizing a category of categories.Colin McLarty - 1991 - Journal of Symbolic Logic 56 (4):1243-1260.
Synthetic Differential Geometry.Anders Kock - 2007 - Bulletin of Symbolic Logic 13 (2):244-245.

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