1 Sets

This chapter (will eventually) contain material on axiomatic set theory, as well as a couple other things.

• Section 1.1: Sets and Functions
  • Subsection 1.1.1: Functions
    • Definition 1.1.1.1.1: Functions
    • Notation 1.1.1.1.2: Additional Notation for Functions
• Section 1.2: The Enrichment of Sets in Classical Truth Values
  • Subsection 1.2.1: $\webleft (-2\webright )$-Categories
    • Definition 1.2.1.1.1: $\webleft (-2\webright )$-Categories
  • Subsection 1.2.2: $\webleft (-1\webright )$-Categories
    • Definition 1.2.2.1.1: $\webleft (-1\webright )$-Categories
    • Remark 1.2.2.1.2: Motivation for $\webleft (-1\webright )$-Categories
    • Definition 1.2.2.1.3: The Poset of Truth Values
    • Notation 1.2.2.1.4: Further Notation for The Poset of Truth Values
    • Proposition 1.2.2.1.5: Cartesian Closedness of the Poset of Truth Values
  • Subsection 1.2.3: $0$-Categories
    • Definition 1.2.3.1.1: $0$-Categories
    • Definition 1.2.3.1.2: $0$-Groupoids
  • Subsection 1.2.4: Tables of Analogies Between Set Theory and Category Theory
    • Remark 1.2.4.1.1: Basic Analogies Between Set Theory and Category Theory
    • Remark 1.2.4.1.2: Analogies Between Set Theory and Category Theory: Powersets and Categories of Presheaves
    • Remark 1.2.4.1.3: Analogies Between Set Theory and Category Theory: Categories of Elements
    • Remark 1.2.4.1.4: Analogies Between Set Theory and Category Theory: Functions Between Powersets and Functors Between Presheaf Categories
    • Remark 1.2.4.1.5: Analogies Between Set Theory and Category Theory: Relations and Profunctors