Theorems · Theorem · category theory

CategoryTheory.Limits.pullbackSymmetry_hom_comp_fst_assoc

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

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

12 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullback