The Clowder Project

9.10 Categories of Categories

• Subsection 9.10.1: Functor Categories
  • Definition 9.10.1.1.1: Functor Categories
  • Proposition 9.10.1.1.2: Properties of Functor Categories
• Subsection 9.10.2: The Category of Categories and Functors
  • Definition 9.10.2.1.1: The Category of Categories and Functors
  • Proposition 9.10.2.1.2: Properties of the Category $\mathsf{Cats}$
• Subsection 9.10.3: The $2$-Category of Categories, Functors, and Natural Transformations
  • Definition 9.10.3.1.1: The $2$-Category of Categories
  • Proposition 9.10.3.1.2: Properties of the 2-Category $\mathsf{Cats}_{\mathsf{2}}$
• Subsection 9.10.4: The Category of Groupoids
  • Definition 9.10.4.1.1: The Category of Small Groupoids
• Subsection 9.10.5: The $2$-Category of Groupoids
  • Definition 9.10.5.1.1: The $2$-Category of Small Groupoids