Set theory for category theory

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.

References in corpus (1)

• Understanding the small object argument

Cited by in corpus (10)

• An Abstract Factorization Theorem and Some Applications
• Fibration Categories are Fibrant Relative Categories
• A new definition of Kuranishi space
• Using the internal language of toposes in algebraic geometry
• Notes on Category Theory with examples from basic mathematics
• Nesting of dynamic systems and mode-dependent networks
• Formulating Categorical Concepts using Classes
• Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory
• RCF4: Inconsistent Quantification
• Motivic Measures through Waldhausen K-Theories