The Clowder Project

Proofs that need to be added at some point:

1. Chapter 4: Tensor Products of Pointed Sets, Theorem 4.5.10.1.1.
2. Chapter 4: Tensor Products of Pointed Sets, Theorem 4.5.11.1.1.
3. Horizontal composition of natural transformations is associative: Chapter 8: Categories, Item 2 of Proposition 8.8.4.1.3.
4. Fully faithful functors are essentially injective: Chapter 8: Categories, Item 3 of Proposition 8.5.3.1.2.

Proofs that would be very nice to be added at some point:

1. Properties of pseudomonic functors: Chapter 8: Categories, Proposition 8.6.4.1.2.
2. Characterisation of fully faithful functors: Chapter 8: Categories, Item 1 of Proposition 8.5.3.1.2.

Proofs that would be nice to be added at some point:

1. Properties of posetal categories: Chapter 8: Categories, Proposition 8.1.3.1.2.
2. The quadruple adjunction between categories and sets: Chapter 8: Categories, Proposition 8.2.1.1.1.
3. Properties of groupoid completions: Chapter 8: Categories, Proposition 8.3.2.1.3.
4. Properties of cores: Chapter 8: Categories, Proposition 8.3.3.1.4.
5. $F_{*}$ faithful iff $F$ faithful: Chapter 8: Categories, Item 1 of Proposition 8.5.1.1.2.
6. $F_{*}$ full iff $F$ full: Chapter 8: Categories, Item 1 of Proposition 8.5.2.1.2.
7. Injective on objects functors are precisely the isocofibrations in $\mathsf{Cats}_{\mathsf{2}}$: Chapter 8: Categories, Item 1 of Proposition 8.7.1.1.2.
8. Characterisations of monomorphisms of categories: Chapter 8: Categories, Item 1 of Proposition 8.6.2.1.2.
9. Epimorphisms of categories are surjective on objects: Chapter 8: Categories, Item 2 of Proposition 8.6.3.1.2.
10. Properties of pseudoepic functors: Chapter 8: Categories, Proposition 8.6.5.1.2.