The Clowder Project

8.9 Categories of Categories

• Subsection 8.9.1: Functor Categories
  • Definition 8.9.1.1.1: Functor Categories
  • Proposition 8.9.1.1.2: Properties of Functor Categories
• Subsection 8.9.2: The Category of Categories and Functors
  • Definition 8.9.2.1.1: The Category of Categories and Functors
  • Proposition 8.9.2.1.2: Properties of the Category $\mathsf{Cats}$
• Subsection 8.9.3: The $2$-Category of Categories, Functors, and Natural Transformations
  • Definition 8.9.3.1.1: The $2$-Category of Categories
  • Proposition 8.9.3.1.2: Properties of the 2-Category $\mathsf{Cats}_{\mathsf{2}}$
• Subsection 8.9.4: The Category of Groupoids
  • Definition 8.9.4.1.1: The Category of Small Groupoids
• Subsection 8.9.5: The $2$-Category of Groupoids
  • Definition 8.9.5.1.1: The $2$-Category of Small Groupoids