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Category of Sets

Table of Contents

1. Overview

Set is the (or a) category with sets as objects and functions between sets as morphisms. This is vague, because we could "parametrize" the category with different choices of axioms that sets should specify, like:

  • First-order vs higher-order logic
  • Impredicative vs predicative mathematics
  • Classical logic vs intuitionistic logic
  • Axiom of choice
  • Replacement or collection principles
  • Smallness structures

…and much, much more! We could fine-tune the axioms of set theory, by adding things like cardinal hypotheses.

Last Updated 2021-06-01 Tue 10:00.