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arXiv:0810.1279math.CT

Set theory for category theory

Michael A. Shulman

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Abstract

Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made can have noticeable effects on what categorical constructions are permissible. In this expository paper we summarize and compare a number of such "set-theoretic foundations for category theory," and describe their implications for the everyday use of category theory. We assume the reader has some basic knowledge of category theory, but little or no prior experience with formal logic or set theory.

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Journal reference
DOI
Subjects
math.CTCategory Theory math.LOLogic

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  1. Types versus sets (and what about categories?) 1 comment

    • Working category theorist here. I wouldn't subscribe to that statement in this strong form, even though I am convinced that various flavors of type theory are a better foundation for mathematics. But this feature doesn't make me despise ZF set theory. In fact, ZF set theory is a…

      IngoBlechschmidView on HNParent context

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