11.9 Natural Transformations
-
Subsection 11.9.1: Transformations
- Definition 11.9.1.1.1: Transformations
- Notation 11.9.1.1.2: The Set of Transformations Between Two Functors
- Remark 11.9.1.1.3: The Set of Transformations as a Product
-
Subsection 11.9.2: Natural Transformations
- Definition 11.9.2.1.1: Natural Transformations
- Remark 11.9.2.1.2: Further Terminology and Notation for Natural Transformations
- Notation 11.9.2.1.3: The Set of Natural Transformations Between Two Functors
- Definition 11.9.2.1.4: Equality of Natural Transformations
-
Subsection 11.9.3: Examples of Natural Transformations
- Example 11.9.3.1.1: Identity Natural Transformations
- Example 11.9.3.1.2: Natural Transformations Between Morphisms of Monoids
-
Subsection 11.9.4: Vertical Composition of Natural Transformations
- Definition 11.9.4.1.1: Vertical Composition of Natural Transformations
- Proposition 11.9.4.1.2: Properties of Vertical Composition of Natural Transformations
-
Subsection 11.9.5: Horizontal Composition of Natural Transformations
- Definition 11.9.5.1.1: Horizontal Composition of Natural Transformations
- Definition 11.9.5.1.2: Whiskering of Functors With Natural Transformations
- Proposition 11.9.5.1.3: Properties of Horizontal Composition of Natural Transformations
-
Subsection 11.9.6: Properties of Natural Transformations
- Proposition 11.9.6.1.1: Natural Transformations as Categorical Homotopies
-
Subsection 11.9.7: Natural Isomorphisms
- Definition 11.9.7.1.1: Natural Isomorphisms
- Proposition 11.9.7.1.2: Properties of Natural Isomorphisms
