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remove square-eq-htpy
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fredrik-bakke committed Dec 6, 2023
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34 changes: 0 additions & 34 deletions src/foundation/commuting-squares-of-maps.lagda.md
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Expand Up @@ -1004,37 +1004,3 @@ module _
( h) =
compute-concat-htpy-precomp H K W h
```

### Naturality of `eq-htpy` for ordinary functions

Consider a map `f : A → B` and two functions `g h : B C`. Then the square

```text
ap (precomp f C)
(g = h) -------------------------> (g ∘ f = h ∘ f)
^ ^
eq-htpy | | eq-htpy
| |
(g ~ h) --------------------------> (g ∘ f ~ h ∘ f)
precomp f (eq-value g h)
```

commutes.

```agda
square-eq-htpy :
{l1 l2 l3 : Level} {A : UU l1} {B : UU l2} {C : UU l3}
(f : A B) (g h : B C)
coherence-square-maps
( precomp-Π f (eq-value g h))
( eq-htpy)
( eq-htpy)
( ap (precomp f C))
square-eq-htpy {C = C} f g h =
coherence-square-inv-vertical
( ap (precomp f C))
( equiv-funext)
( equiv-funext)
( precomp-Π f (eq-value g h))
( square-htpy-eq f g h)
```

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