The Clowder Project

8.8 Natural Transformations

• Subsection 8.8.1: Transformations
  • Definition 8.8.1.1.1: Transformations
  • Notation 8.8.1.1.2: The Set of Transformations Between Two Functors
• Subsection 8.8.2: Natural Transformations
  • Definition 8.8.2.1.1: Natural Transformations
  • Remark 8.8.2.1.2: Picturing Natural Transformations in Diagrams
  • Notation 8.8.2.1.3: The Set of Natural Transformations Between Two Functors
  • Example 8.8.2.1.4: Identity Natural Transformations
  • Definition 8.8.2.1.5: Equality of Natural Transformations
• Subsection 8.8.3: Vertical Composition of Natural Transformations
  • Definition 8.8.3.1.1: Vertical Composition of Natural Transformations
  • Proposition 8.8.3.1.2: Properties of Vertical Composition of Natural Transformations
• Subsection 8.8.4: Horizontal Composition of Natural Transformations
  • Definition 8.8.4.1.1: Horizontal Composition of Natural Transformations
  • Definition 8.8.4.1.2: Whiskering of Functors With Natural Transformations
  • Proposition 8.8.4.1.3: Properties of Horizontal Composition of Natural Transformations
• Subsection 8.8.5: Properties of Natural Transformations
  • Proposition 8.8.5.1.1: Natural Transformations as Categorical Homotopies
• Subsection 8.8.6: Natural Isomorphisms
  • Definition 8.8.6.1.1: Natural Isomorphisms
  • Proposition 8.8.6.1.2: Properties of Natural Isomorphisms