Theorems · Theorem · category theory

CategoryTheory.Limits.pullbackRightPullbackFstIso_hom_fst_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {W X Y Z : C} (f : X ⟶ Z) (g : Y ⟶ Z) (f' : W ⟶ X)
  [inst_1 : CategoryTheory.Limits.HasPullback f g]
  [inst_2 : CategoryTheory.Limits.HasPullback f' (CategoryTheory.Limits.pullback.fst f g)] {Z_1 : C} (h : W ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullbackRightPullbackFstIso f g f').hom
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.pullback.fst (CategoryTheory.CategoryStruct.comp f' f) g) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst f' (CategoryTheory.Limits.pullback.fst f g))
      h

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting

Cited by

11 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasPullback