The Clowder Project

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