11.5 Functors
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Subsection 11.5.1: Foundations
- Definition 11.5.1.1.1: Functors
- Notation 11.5.1.1.2: Subscript and Superscript Notation for Functors
- Notation 11.5.1.1.3: Additional Notation for Functors
- Example 11.5.1.1.4: Identity Functors
- Definition 11.5.1.1.5: Composition of Functors
- Proposition 11.5.1.1.6: Elementary Properties of Functors
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Subsection 11.5.2: Contravariant Functors
- Definition 11.5.2.1.1: Contravariant Functors
- Remark 11.5.2.1.2: Unwinding Definition 11.5.2.1.1
- Remark 11.5.2.1.3: On the Term Contravariant Functor
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Subsection 11.5.3: Forgetful Functors
- Definition 11.5.3.1.1: Forgetful Functors
- Remark 11.5.3.1.2: Unwinding Definition 11.5.3.1.1
- Example 11.5.3.1.3: Forgetful Functors That Forget Structure
- Example 11.5.3.1.4: Forgetful Functors That Forget Properties
- Notation 11.5.3.1.5: Notation For Forgetful Functors That Forget Structure
- Remark 11.5.3.1.6: Pronunciation of the Words in Notation 11.5.3.1.5
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Subsection 11.5.4: The Natural Transformation Associated to a Functor
- Definition 11.5.4.1.1: The Natural Transformation Associated to a Functor
- Proposition 11.5.4.1.2: Properties of Natural Transformations Associated to Functors
