This is an archived version pinned as of the submission of my master's thesis. An up-to-date version may be found online.

Commuting squares of morphisms in precategories

module category-theory.commuting-squares-of-morphisms-in-precategories where

open import category-theory.commuting-squares-of-morphisms-in-set-magmoids
open import category-theory.precategories

open import foundation.universe-levels

Idea

A square of morphisms

  x ------> y
  |         |
  |         |
  ∨         ∨
  z ------> w

in a precategory C is said to commute if there is an identification between both composites:

  bottom ∘ left ＝ right ∘ top.

Definitions

coherence-square-hom-Precategory :
  {l1 l2 : Level} (C : Precategory l1 l2) {x y z w : obj-Precategory C}
  (top : hom-Precategory C x y)
  (left : hom-Precategory C x z)
  (right : hom-Precategory C y w)
  (bottom : hom-Precategory C z w) →
  UU l2
coherence-square-hom-Precategory C =
  coherence-square-hom-Set-Magmoid (set-magmoid-Precategory C)