Theorems · Theorem · category theory

CategoryTheory.Limits.pullback.congrHom_hom

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f₁ f₂ : X ⟶ Z} {g₁ g₂ : Y ⟶ Z} (h₁ : f₁ = f₂)
  (h₂ : g₁ = g₂) [inst_1 : CategoryTheory.Limits.HasPullback f₁ g₁] [inst_2 : CategoryTheory.Limits.HasPullback f₂ g₂],
  (CategoryTheory.Limits.pullback.congrHom h₁ h₂).hom =
    CategoryTheory.Limits.pullback.map f₁ g₁ f₂ g₂ (CategoryTheory.CategoryStruct.id X)
      (CategoryTheory.CategoryStruct.id Y) (CategoryTheory.CategoryStruct.id Z) ⋯ ⋯

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

11 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasPullback