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EgbertRijke committed Dec 3, 2024
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Expand Up @@ -31,8 +31,8 @@ Consider two

A binary dependent globular type `K` over reflexive globular types `G` and `H`
is said to be
{{#concept "reflexive" Disambiguation="binary dependent globular type"}} if it
comes equipped with
{{#concept "reflexive" Disambiguation="binary dependent globular type" Agda=is-reflexive-Binary-Dependent-Globular-Type}}
if it comes equipped with

```text
refl K : {x : G₀} {y : H₀} (u : K₀ x y) K₁ (refl G x) (refl G y) u u,
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Expand Up @@ -51,13 +51,16 @@ record
{l1 l2 : Level} (G : Globular-Type l1 l2) : UU (l1 ⊔ l2)
where
coinductive

field
comp-binary-globular-map-composition-Globular-Type :
{x y z : 0-cell-Globular-Type G}
binary-globular-map
( 1-cell-globular-type-Globular-Type G y z)
( 1-cell-globular-type-Globular-Type G x y)
( 1-cell-globular-type-Globular-Type G x z)

field
composition-1-cell-globular-type-Globular-Type :
{x y : 0-cell-Globular-Type G}
composition-Globular-Type
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Expand Up @@ -70,7 +70,6 @@ record
(H : Large-Reflexive-Globular-Type α2 β2)
(f : large-globular-map-Large-Reflexive-Globular-Type γ G H) : UUω
where
coinductive

field
preserves-refl-1-cell-is-colax-reflexive-large-globular-map :
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Expand Up @@ -58,7 +58,6 @@ record
(H : Large-Transitive-Globular-Type α2 β2)
(f : large-globular-map-Large-Transitive-Globular-Type γ G H) : UUω
where
coinductive

field
preserves-comp-1-cell-is-colax-transitive-large-globular-map :
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Expand Up @@ -70,7 +70,6 @@ record
(H : Large-Reflexive-Globular-Type α2 β2)
(f : large-globular-map-Large-Reflexive-Globular-Type γ G H) : UUω
where
coinductive

field
preserves-refl-1-cell-is-lax-reflexive-large-globular-map :
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Expand Up @@ -58,7 +58,6 @@ record
(H : Large-Transitive-Globular-Type α2 β2)
(f : large-globular-map-Large-Transitive-Globular-Type γ G H) : UUω
where
coinductive

field
preserves-comp-1-cell-is-lax-transitive-large-globular-map :
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1 change: 0 additions & 1 deletion src/globular-types/large-reflexive-globular-maps.lagda.md
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Expand Up @@ -60,7 +60,6 @@ record
(f : large-globular-map-Large-Reflexive-Globular-Type γ G H) :
UUω
where
coinductive

field
preserves-refl-1-cell-preserves-refl-large-globular-map :
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1 change: 0 additions & 1 deletion src/globular-types/large-transitive-globular-maps.lagda.md
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Expand Up @@ -52,7 +52,6 @@ record
(H : Large-Transitive-Globular-Type α2 β2)
(f : large-globular-map-Large-Transitive-Globular-Type γ G H) : UUω
where
coinductive

field
preserves-comp-1-cell-is-transitive-large-globular-map :
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2 changes: 1 addition & 1 deletion src/globular-types/superglobular-types.lagda.md
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Expand Up @@ -70,7 +70,7 @@ The low-dimensional data of a superglobular type is therefore as follows:
G₃ : {x y : G₀} {s t : G₁ x y} (u v : G₂ s t) Type
H₂ : {x x' y y' : G₀} {s s' : G₁ x x'} {t t' : G₁ y y'}
(p : G₂ s s') (q : G₂ t t') H₁ s t H₁ s' t' Type
e₂ : {x y : G₀} {s t : H₀ x y} {u v : H₁
e₂ : {x y : G₀} {s t : H₀ x y} {u v : H₁ (refl G x) (refl G y) s t}
H₂ (refl G x) (refl G y) u v ≃ G₃ (e₁ u) (e₁ v)
```

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