Subsection 10.1.1 (01CT): Omitted Proofs To Add

There’s a very large number of omitted proofs throughout these notes. Here I list them in decreasing order of how nice it would be to add them.

Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

Proofs that need to be added at some point:

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

Properties of pseudomonic functors: Chapter 8: Categories, Proposition 8.6.4.1.2.
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:

Properties of posetal categories: Chapter 8: Categories, Proposition 8.1.3.1.2.
The quadruple adjunction between categories and sets: Chapter 8: Categories, Proposition 8.2.1.1.1.
Properties of groupoid completions: Chapter 8: Categories, Proposition 8.3.2.1.3.
Properties of cores: Chapter 8: Categories, Proposition 8.3.3.1.4.
$F_{*}$ faithful iff $F$ faithful: Chapter 8: Categories, Item 1 of Proposition 8.5.1.1.2.
$F_{*}$ full iff $F$ full: Chapter 8: Categories, Item 1 of Proposition 8.5.2.1.2.
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.
Characterisations of monomorphisms of categories: Chapter 8: Categories, Item 1 of Proposition 8.6.2.1.2.
Epimorphisms of categories are surjective on objects: Chapter 8: Categories, Item 2 of Proposition 8.6.3.1.2.
Properties of pseudoepic functors: Chapter 8: Categories, Proposition 8.6.5.1.2.

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