Set theory for category theory

By Michael Shulman. 2008

49 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7382f4f089d63ea4129445aca7f246782bb0a0af

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Yonatan Harpaz
2. Denis-Charles Cisinski
3. Ilan Barnea
4. Geoffroy Horel

In Computational Theory and Mathematics

1. Yonatan Harpaz
2. Denis-Charles Cisinski
3. Ilan Barnea
4. Geoffroy Horel

In Mathematical Physics

1. Yonatan Harpaz
2. Denis-Charles Cisinski
3. Ilan Barnea
4. Geoffroy Horel
5. Gonçalo Tabuada
6. L. Cohn
7. Moritz Groth
8. Christian Sattler

Citations in the corpus

• Higher Categories and Homotopical Algebra (2019, methodology): “We refer to [Shu08] for an excellent account on the possible set-theoretic frameworks for Category Theory.”
• Pro-categories in homotopy theory (2015, methodology): “We refer the reader to [Sh08] for a detailed account of various possible set theoretical foundations for category theory.”