12.1 Presheaves
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Subsection 12.1.1: Foundations
- Definition 12.1.1.1.1: Presheaves on a Category
- Example 12.1.1.1.2: Presheaves on One-Object Categories
- Definition 12.1.1.1.3: Morphisms of Presheaves
- Definition 12.1.1.1.4: The Category of Presheaves on a Category
- Remark 12.1.1.1.5: Unwinding Definition 12.1.1.1.4
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Subsection 12.1.2: Representable Presheaves
- Definition 12.1.2.1.1: Representable Presheaves
- Example 12.1.2.1.2: Representable Presheaves on One-Object Categories
- Proposition 12.1.2.1.3: Uniqueness of Representing Objects Up to Isomorphism
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Subsection 12.1.3: Representable Natural Transformations
- Definition 12.1.3.1.1: Representable Natural Transformations
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Subsection 12.1.4: The Yoneda Embedding
- Definition 12.1.4.1.1: The Yoneda Embedding
- Remark 12.1.4.1.2: On the Usage of ${\text{よ}}$ to Denote the Yoneda Embedding
- Proposition 12.1.4.1.3: Properties of the Yoneda Embedding
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Subsection 12.1.5: The Yoneda Lemma
- Theorem 12.1.5.1.1: The Yoneda Lemma
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Subsection 12.1.6: Properties of Categories of Presheaves
- Proposition 12.1.6.1.1: Properties of Categories of Presheaves
