Theorems · Theorem · category theory

CategoryTheory.Limits.pullback.hom_ext

∀ {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] {W : C} {k l : W ⟶ CategoryTheory.Limits.pullback f g},
  CategoryTheory.CategoryStruct.comp k (CategoryTheory.Limits.pullback.fst f g) =
      CategoryTheory.CategoryStruct.comp l (CategoryTheory.Limits.pullback.fst f g) →
    CategoryTheory.CategoryStruct.comp k (CategoryTheory.Limits.pullback.snd f g) =
        CategoryTheory.CategoryStruct.comp l (CategoryTheory.Limits.pullback.snd f g) →
      k = l

Two morphisms into a pullback are equal if their compositions with the pullback morphisms are equal

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

63 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullback