Theorems · Theorem · category theory

CategoryTheory.Limits.pullbackLeftPullbackSndIso_hom_fst

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {W X Y Z : C} (f : X ⟶ Z) (g : Y ⟶ Z) (g' : W ⟶ Y)
  [inst_1 : CategoryTheory.Limits.HasPullback f g]
  [inst_2 : CategoryTheory.Limits.HasPullback (CategoryTheory.Limits.pullback.snd f g) g'],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullbackLeftPullbackSndIso f g g').hom
      (CategoryTheory.Limits.pullback.fst f (CategoryTheory.CategoryStruct.comp g' g)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst (CategoryTheory.Limits.pullback.snd f g) g')
      (CategoryTheory.Limits.pullback.fst f g)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting

Cited by

3 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasPullback