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Hofmann-Streicher universes for graphs and globular types #1196

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645fdb9
work on universal objects
Sep 24, 2024
c2abb43
Merge branch 'master' of github.com:UniMath/agda-unimath into globular
Sep 24, 2024
3e17ca8
adding infrastructure for globular types
EgbertRijke Sep 28, 2024
9bac61a
work
EgbertRijke Oct 9, 2024
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Merge branch 'master' of github.com:UniMath/agda-unimath into globular
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72731cb
computation of the universal globular type, and correspondence of dep…
EgbertRijke Oct 11, 2024
bb31cac
reflexive globular maps
EgbertRijke Oct 13, 2024
f56cc6a
sections and pi
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70213c1
typo
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5e0fac9
Merge branch 'master' of github.com:UniMath/agda-unimath into globular
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90651f3
make pre-commit
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0285824
working towards duality of directed graphs
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duality for directed graphs
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c98f6e2
fibers and sections
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cbc1744
wild category of pointed types
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8c3e39f
mention the categorical laws, which were duplicated
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9c4ac74
small edits
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7629b7d
work
EgbertRijke Oct 17, 2024
45f2d8b
refactor reflexive and transitive globular types
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f445848
lots of work
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b9ea44a
maps
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cab0051
colax functors of noncoherent wild higher precategories
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fe3a463
Merge branch 'master' of github.com:UniMath/agda-unimath into globular
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b4a6ea7
Merge branch 'master' of github.com:UniMath/agda-unimath into globular
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b16dbd3
work
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c9f1f92
large (co)lax reflexive globular maps
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3e20e46
variations of transitive globular maps
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d958890
refacotr colax functors of noncoherent large wild precategories
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f2bec34
make pre-commit
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d019b03
fix concept macros
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make pre-commit
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f340e81
reflexive graphs
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5236141
reflexive graphs
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7d88972
Merge branch 'master' of github.com:UniMath/agda-unimath into globular
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0773c07
make pre-commit
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04893a9
fix bugs
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work on broken links
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work on reflexive graphs
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bugs
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work
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a889dcd
Merge branch 'master' of github.com:UniMath/agda-unimath into globular
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6221b38
fibers of morphisms of reflexive graphs
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make pre-commit
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c8b9596
typo
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7851d96
Merge branch 'master' of github.com:UniMath/agda-unimath into globular
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3aabeb8
dependent products of reflexive graphs
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b39c097
minor edit
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077e3a9
Merge branch 'master' of github.com:UniMath/agda-unimath into globular
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review comments
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7d1a041
base change of universal dependent directed graph
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upstream master
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9336e8e
Merge branch 'master' of github.com:UniMath/agda-unimath into globular
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ec6eec8
some review comments
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9b9511e
-> laxly
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a0bda74
review comment
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3f48134
typo
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f070148
-> lax
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d72ea0b
concept
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a3a945c
pointwise extensions of families of globular types
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221e5d8
file for extensive globular types
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392b591
superglobular types
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d3789b6
superglobular types
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4626f95
uniform
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668bd20
structure
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45a4ea8
removing the itemization formatting in record
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unbolden text with added colon
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774d2ae
correcting an incorrect definition of discrete relations
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bf7aab7
Update src/foundation/discrete-relations.lagda.md
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79b6cf2
fix broken Agda reference
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0b304f7
Merge branch 'discrete-graphs' of github.com:EgbertRijke/agda-unimath…
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bc2b2be
factor out discrete globular types
EgbertRijke Nov 15, 2024
7d0819d
implementing discreteness via adjointness
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fdd6436
bugs
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bugs
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3189352
adjointness for discrete directed graphs
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f123e98
Merge branch 'master' of github.com:UniMath/agda-unimath into globular
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edit discrete reflexive globular types
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discrete globular types
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ᵣ to refl
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partially revert long copattern matchings
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discrete dependent reflexive graphs
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discrete dependent reflexive globular types
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4 changes: 2 additions & 2 deletions src/structured-types/large-reflexive-globular-types.lagda.md
Original file line number Diff line number Diff line change
Expand Up @@ -107,7 +107,7 @@ record
where
```

- The underlying large globular type of a large reflexive globular type
**The underlying large globular type of a large reflexive globular type**

```agda
field
Expand Down Expand Up @@ -274,7 +274,7 @@ record
large-globular-type-Large-Reflexive-Globular-Type
```

- The reflexivity structure of a large reflexive globular type
**The reflexivity structure of a large reflexive globular type**

```agda
field
Expand Down
6 changes: 3 additions & 3 deletions src/structured-types/reflexive-globular-types.lagda.md
Original file line number Diff line number Diff line change
Expand Up @@ -123,7 +123,7 @@ record
where
```

- The underlying globular type of a reflexive globular type
**The underlying globular type of a reflexive globular type**

```agda
field
Expand Down Expand Up @@ -158,7 +158,7 @@ record
( globular-type-Reflexive-Globular-Type)
```

- The reflexivity structure of a reflexive globular type
**The reflexivity structure of a reflexive globular type**

```agda
field
Expand Down Expand Up @@ -196,7 +196,7 @@ record
refl-Reflexive-Globular-Type
```

- The reflexive globular type of 1-cells of a reflexive globular type
**The reflexive globular type of 1-cells of a reflexive globular type**

```agda
1-cell-reflexive-globular-type-Reflexive-Globular-Type :
Expand Down
4 changes: 2 additions & 2 deletions src/structured-types/transitive-globular-types.lagda.md
Original file line number Diff line number Diff line change
Expand Up @@ -114,7 +114,7 @@ record
make-Transitive-Globular-Type
```

- The underlying globular type of a transitive globular type
**The underlying globular type of a transitive globular type**

```agda
field
Expand Down Expand Up @@ -167,7 +167,7 @@ record
( globular-type-Transitive-Globular-Type)
```

- The composition structure of a transitive globular type
**The composition structure of a transitive globular type**

```agda
field
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -209,7 +209,7 @@ record
where
```

- The underlying large globular map of a colax functor
**The underlying large globular map of a colax functor**

```agda
field
Expand Down Expand Up @@ -268,7 +268,7 @@ record
( map-colax-functor-Noncoherent-Large-Wild-Higher-Precategory)
```

- Preservation of the identity structure
**Preservation of the identity structure**

```agda
preserves-id-structure-colax-functor-Noncoherent-Large-Wild-Higher-Precategory :
Expand Down Expand Up @@ -319,7 +319,7 @@ record
is-colax-functor-colax-functor-Noncoherent-Large-Wild-Higher-Precategory
```

- Preservation of the composition structure
**Preservation of the composition structure**

```agda
preserves-comp-structure-colax-functor-Noncoherent-Large-Wild-Higher-Precategory :
Expand Down Expand Up @@ -375,7 +375,7 @@ record
is-colax-functor-colax-functor-Noncoherent-Large-Wild-Higher-Precategory
```

- The globular map on hom-types is again a colax functor
**The globular map on hom-types is again a colax functor**

```agda
is-colax-functor-hom-colax-functor-colax-functor-Noncoherent-Large-Wild-Higher-Precategory :
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -192,7 +192,7 @@ colax-functor-Noncoherent-Wild-Higher-Precategory 𝒜 ℬ =
( is-colax-functor-Noncoherent-Wild-Higher-Precategory 𝒜 ℬ)
```

- The action of colax functors on objects, morphisms, and higher morphisms
**The action of colax functors on objects, morphisms, and higher morphisms**

```agda
module _
Expand Down Expand Up @@ -248,7 +248,7 @@ module _
is-colax-functor-colax-functor-Noncoherent-Wild-Higher-Precategory = pr2 F
```

- Preservation by colax functors of identity morphisms
**Preservation by colax functors of identity morphisms**

```agda
preserves-id-hom-colax-functor-Noncoherent-Wild-Higher-Precategory :
Expand All @@ -275,7 +275,7 @@ module _
is-colax-functor-colax-functor-Noncoherent-Wild-Higher-Precategory
```

- Preservation by colax functors of composition
**Preservation by colax functors of composition**

```agda
preserves-comp-hom-colax-functor-Noncoherent-Wild-Higher-Precategory :
Expand Down Expand Up @@ -305,8 +305,8 @@ module _
is-colax-functor-colax-functor-Noncoherent-Wild-Higher-Precategory
```

- The induced colax functor on the wild category of morphisms between two
objects
**The induced colax functor on the wild category of morphisms between two **
**objects**
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```agda
hom-colax-functor-colax-functor-Noncoherent-Wild-Higher-Precategory :
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -79,15 +79,15 @@ record
where
```

- The underlying large globular type of a noncoherent large wild precategory
**The underlying large globular type of a noncoherent large wild precategory**

```agda
field
large-globular-type-Noncoherent-Large-Wild-Higher-Precategory :
Large-Globular-Type α β
```

- The type of objects of a noncoherent large wild higher precategory
**The type of objects of a noncoherent large wild higher precategory**

```agda
obj-Noncoherent-Large-Wild-Higher-Precategory : (l : Level) → UU (α l)
Expand All @@ -96,8 +96,8 @@ record
large-globular-type-Noncoherent-Large-Wild-Higher-Precategory
```

- The globular type of morphisms between two objects in a noncoherent large wild
higher precategory
**The globular type of morphisms between two objects in a noncoherent large **
**wild higher precategory**

```agda
hom-globular-type-Noncoherent-Large-Wild-Higher-Precategory :
Expand All @@ -119,8 +119,8 @@ record
large-globular-type-Noncoherent-Large-Wild-Higher-Precategory
```

- The globular structure on the type of objects of a noncoherent large wild
higher precategory
**The globular structure on the type of objects of a noncoherent large wild **
**higher precategory**

```agda
globular-structure-obj-Noncoherent-Large-Wild-Higher-Precategory :
Expand All @@ -130,8 +130,8 @@ record
large-globular-type-Noncoherent-Large-Wild-Higher-Precategory
```

- The globular type of 2-morphisms is a noncoherent large wild higher
precategory
**The globular type of 2-morphisms is a noncoherent large wild higher **
**precategory**

```agda
2-hom-globular-type-Noncoherent-Large-Wild-Higher-Precategory :
Expand All @@ -154,8 +154,8 @@ record
large-globular-type-Noncoherent-Large-Wild-Higher-Precategory
```

- The globular structure on the type of morphisms between two objects in a
noncoherent large wild higher precategory
**The globular structure on the type of morphisms between two objects in a **
**noncoherent large wild higher precategory**

```agda
globular-structure-hom-Noncoherent-Large-Wild-Higher-Precategory :
Expand All @@ -170,8 +170,8 @@ record
large-globular-type-Noncoherent-Large-Wild-Higher-Precategory
```

- The globular type of 3-morphisms in a noncoherent large wild higher
precategory
**The globular type of 3-morphisms in a noncoherent large wild higher **
**precategory**

```agda
3-hom-globular-type-Noncoherent-Large-Wild-Higher-Precategory :
Expand All @@ -198,8 +198,8 @@ record
large-globular-type-Noncoherent-Large-Wild-Higher-Precategory
```

- The globular structure on the type of 2-morphisms in a noncoherent large wild
higher precategory
**The globular structure on the type of 2-morphisms in a noncoherent large **
**wild higher precategory**

```agda
globular-structure-2-hom-Noncoherent-Large-Wild-Higher-Precategory :
Expand All @@ -215,8 +215,8 @@ record
large-globular-type-Noncoherent-Large-Wild-Higher-Precategory
```

- The structure of identity morphisms in a noncoherent large wild higher
precategory
**The structure of identity morphisms in a noncoherent large wild higher **
**precategory**

```agda
field
Expand Down Expand Up @@ -264,7 +264,7 @@ record
id-structure-Noncoherent-Large-Wild-Higher-Precategory
```

- The structure of composition in a noncoherent large wild higher precategory
**The structure of composition in a noncoherent large wild higher precategory**

```agda
field
Expand Down Expand Up @@ -320,8 +320,8 @@ record
comp-structure-Noncoherent-Large-Wild-Higher-Precategory
```

- The noncoherent wild higher precategory of morphisms between two object in a
noncoherent large wild higher precategory
**The noncoherent wild higher precategory of morphisms between two object in **
**a noncoherent large wild higher precategory**

```agda
hom-noncoherent-wild-higher-precategory-Noncoherent-Large-Wild-Higher-Precategory :
Expand All @@ -338,8 +338,8 @@ record
( comp-structure-hom-globular-type-Noncoherent-Large-Wild-Higher-Precategory)
```

- The underlying reflexive globular type of a noncoherent large wild higher
precategory
**The underlying reflexive globular type of a noncoherent large wild higher **
**precategory**

```agda
large-reflexive-globular-type-Noncoherent-Large-Wild-Higher-Precategory :
Expand All @@ -352,8 +352,8 @@ record
id-structure-Noncoherent-Large-Wild-Higher-Precategory
```

- The underlying transitive globular type of a noncoherent large wild higher
precategory
**The underlying transitive globular type of a noncoherent large wild higher **
**precategory**

```agda
large-transitive-globular-type-Noncoherent-Large-Wild-Higher-Precategory :
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -92,7 +92,7 @@ module _
0-cell-Globular-Type globular-type-Noncoherent-Wild-Higher-Precategory
```

- Morphisms in a noncoherent wild higher precategory
**Morphisms in a noncoherent wild higher precategory**

```agda
hom-globular-type-Noncoherent-Wild-Higher-Precategory :
Expand All @@ -110,7 +110,7 @@ module _
1-cell-Globular-Type globular-type-Noncoherent-Wild-Higher-Precategory
```

- Identity morphisms in a noncoherent wild higher precategory
**Identity morphisms in a noncoherent wild higher precategory**

```agda
id-structure-Noncoherent-Wild-Higher-Precategory :
Expand Down Expand Up @@ -152,7 +152,7 @@ module _
( y)
```

- Composition in a noncoherent wild higher precategory
**Composition in a noncoherent wild higher precategory**

```agda
comp-structure-Noncoherent-Wild-Higher-Precategory :
Expand Down Expand Up @@ -197,8 +197,8 @@ module _
( y)
```

- The noncoherent wild higher precategory of morphisms between two objects in a
noncoherent wild higher precategory
**The noncoherent wild higher precategory of morphisms between two objects in **
**a noncoherent wild higher precategory**

```agda
hom-noncoherent-wild-higher-precategory-Noncoherent-Wild-Higher-Precategory :
Expand All @@ -212,7 +212,7 @@ module _
( comp-structure-hom-globular-type-Noncoherent-Wild-Higher-Precategory)
```

- 2-Morphisms in a noncoherent wild higher precategory
**2-Morphisms in a noncoherent wild higher precategory**

```agda
2-hom-Noncoherent-Wild-Higher-Precategory :
Expand Down Expand Up @@ -242,7 +242,7 @@ module _
comp-structure-Noncoherent-Wild-Higher-Precategory
```

- 3-Morphisms in a noncoherent wild higher precategory
**3-Morphisms in a noncoherent wild higher precategory**

```agda
3-hom-Noncoherent-Wild-Higher-Precategory :
Expand Down
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