The Clowder Project

9.3 The Quadruple Adjunction With Sets

• Subsection 9.3.1: Statement
  • Proposition 9.3.1.1.1: The Quadruple Adjunction Between $\mathsf{Sets}$ and $\mathsf{Cats}$
• Subsection 9.3.2: Connected Components and Connected Categories
  • Subsubsection 9.3.2.1: Connected Components of Categories
    • Definition 9.3.2.1.1: Connected Components of Categories
  • Subsubsection 9.3.2.2: Sets of Connected Components of Categories
    • Definition 9.3.2.2.1: Sets of Connected Components of Categories
    • Proposition 9.3.2.2.2: Properties of Sets of Connected Components
  • Subsubsection 9.3.2.3: Connected Categories
    • Definition 9.3.2.3.1: Connected Categories
• Subsection 9.3.3: Discrete Categories
  • Definition 9.3.3.1.1: Discrete Categories
  • Proposition 9.3.3.1.2: Properties of Discrete Categories on Sets
• Subsection 9.3.4: Indiscrete Categories
  • Definition 9.3.4.1.1: Indiscrete Categories
  • Proposition 9.3.4.1.2: Properties of Indiscrete Categories on Sets