diff --git a/src/foundation/commuting-squares-of-maps.lagda.md b/src/foundation/commuting-squares-of-maps.lagda.md index 36b262e97b..cd859525e3 100644 --- a/src/foundation/commuting-squares-of-maps.lagda.md +++ b/src/foundation/commuting-squares-of-maps.lagda.md @@ -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) -```