/
category-theory.lagda.md
157 lines (150 loc) · 9.38 KB
/
category-theory.lagda.md
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
# Category theory
## Examples of categories and large categories
{{#include tables/categories.md}}
## Examples of precategories and large precategories
{{#include tables/precategories.md}}
## Files in the category theory folder
```agda
module category-theory where
open import category-theory.adjunctions-large-categories public
open import category-theory.adjunctions-large-precategories public
open import category-theory.anafunctors-categories public
open import category-theory.anafunctors-precategories public
open import category-theory.augmented-simplex-category public
open import category-theory.categories public
open import category-theory.category-of-functors public
open import category-theory.category-of-functors-from-small-to-large-categories public
open import category-theory.category-of-maps-categories public
open import category-theory.category-of-maps-from-small-to-large-categories public
open import category-theory.commuting-squares-of-morphisms-in-large-precategories public
open import category-theory.commuting-squares-of-morphisms-in-precategories public
open import category-theory.commuting-squares-of-morphisms-in-set-magmoids public
open import category-theory.composition-operations-on-binary-families-of-sets public
open import category-theory.conservative-functors-precategories public
open import category-theory.constant-functors public
open import category-theory.copresheaf-categories public
open import category-theory.coproducts-in-precategories public
open import category-theory.cores-categories public
open import category-theory.cores-precategories public
open import category-theory.dependent-products-of-categories public
open import category-theory.dependent-products-of-large-categories public
open import category-theory.dependent-products-of-large-precategories public
open import category-theory.dependent-products-of-precategories public
open import category-theory.discrete-categories public
open import category-theory.embedding-maps-precategories public
open import category-theory.embeddings-precategories public
open import category-theory.endomorphisms-in-categories public
open import category-theory.endomorphisms-in-precategories public
open import category-theory.epimorphisms-in-large-precategories public
open import category-theory.equivalences-of-categories public
open import category-theory.equivalences-of-large-precategories public
open import category-theory.equivalences-of-precategories public
open import category-theory.essential-fibers-of-functors-precategories public
open import category-theory.essentially-injective-functors-precategories public
open import category-theory.essentially-surjective-functors-precategories public
open import category-theory.exponential-objects-precategories public
open import category-theory.faithful-functors-precategories public
open import category-theory.faithful-maps-precategories public
open import category-theory.full-functors-precategories public
open import category-theory.full-large-subcategories public
open import category-theory.full-large-subprecategories public
open import category-theory.full-maps-precategories public
open import category-theory.full-subcategories public
open import category-theory.full-subprecategories public
open import category-theory.fully-faithful-functors-precategories public
open import category-theory.fully-faithful-maps-precategories public
open import category-theory.function-categories public
open import category-theory.function-precategories public
open import category-theory.functors-categories public
open import category-theory.functors-from-small-to-large-categories public
open import category-theory.functors-from-small-to-large-precategories public
open import category-theory.functors-large-categories public
open import category-theory.functors-large-precategories public
open import category-theory.functors-nonunital-precategories public
open import category-theory.functors-precategories public
open import category-theory.functors-set-magmoids public
open import category-theory.gaunt-categories public
open import category-theory.groupoids public
open import category-theory.homotopies-natural-transformations-large-precategories public
open import category-theory.indiscrete-precategories public
open import category-theory.initial-category public
open import category-theory.initial-objects-large-categories public
open import category-theory.initial-objects-large-precategories public
open import category-theory.initial-objects-precategories public
open import category-theory.isomorphism-induction-categories public
open import category-theory.isomorphism-induction-precategories public
open import category-theory.isomorphisms-in-categories public
open import category-theory.isomorphisms-in-large-categories public
open import category-theory.isomorphisms-in-large-precategories public
open import category-theory.isomorphisms-in-precategories public
open import category-theory.isomorphisms-in-subprecategories public
open import category-theory.large-categories public
open import category-theory.large-function-categories public
open import category-theory.large-function-precategories public
open import category-theory.large-precategories public
open import category-theory.large-subcategories public
open import category-theory.large-subprecategories public
open import category-theory.maps-categories public
open import category-theory.maps-from-small-to-large-categories public
open import category-theory.maps-from-small-to-large-precategories public
open import category-theory.maps-precategories public
open import category-theory.maps-set-magmoids public
open import category-theory.monomorphisms-in-large-precategories public
open import category-theory.natural-isomorphisms-functors-categories public
open import category-theory.natural-isomorphisms-functors-large-precategories public
open import category-theory.natural-isomorphisms-functors-precategories public
open import category-theory.natural-isomorphisms-maps-categories public
open import category-theory.natural-isomorphisms-maps-precategories public
open import category-theory.natural-numbers-object-precategories public
open import category-theory.natural-transformations-functors-categories public
open import category-theory.natural-transformations-functors-from-small-to-large-categories public
open import category-theory.natural-transformations-functors-from-small-to-large-precategories public
open import category-theory.natural-transformations-functors-large-categories public
open import category-theory.natural-transformations-functors-large-precategories public
open import category-theory.natural-transformations-functors-precategories public
open import category-theory.natural-transformations-maps-categories public
open import category-theory.natural-transformations-maps-from-small-to-large-precategories public
open import category-theory.natural-transformations-maps-precategories public
open import category-theory.nonunital-precategories public
open import category-theory.one-object-precategories public
open import category-theory.opposite-categories public
open import category-theory.opposite-large-precategories public
open import category-theory.opposite-precategories public
open import category-theory.opposite-preunivalent-categories public
open import category-theory.precategories public
open import category-theory.precategory-of-functors public
open import category-theory.precategory-of-functors-from-small-to-large-precategories public
open import category-theory.precategory-of-maps-from-small-to-large-precategories public
open import category-theory.precategory-of-maps-precategories public
open import category-theory.pregroupoids public
open import category-theory.presheaf-categories public
open import category-theory.preunivalent-categories public
open import category-theory.products-in-precategories public
open import category-theory.products-of-precategories public
open import category-theory.pseudomonic-functors-precategories public
open import category-theory.pullbacks-in-precategories public
open import category-theory.replete-subprecategories public
open import category-theory.representable-functors-categories public
open import category-theory.representable-functors-large-precategories public
open import category-theory.representable-functors-precategories public
open import category-theory.representing-arrow-category public
open import category-theory.restrictions-functors-cores-precategories public
open import category-theory.rigid-objects-categories public
open import category-theory.rigid-objects-precategories public
open import category-theory.set-magmoids public
open import category-theory.sieves-in-categories public
open import category-theory.simplex-category public
open import category-theory.slice-precategories public
open import category-theory.split-essentially-surjective-functors-precategories public
open import category-theory.strict-categories public
open import category-theory.structure-equivalences-set-magmoids public
open import category-theory.subcategories public
open import category-theory.subprecategories public
open import category-theory.subterminal-precategories public
open import category-theory.terminal-category public
open import category-theory.terminal-objects-precategories public
open import category-theory.wide-subcategories public
open import category-theory.wide-subprecategories public
open import category-theory.yoneda-lemma-categories public
open import category-theory.yoneda-lemma-precategories public
```