Theorems · Theorem · category theory

CategoryTheory.Limits.PullbackCone.equalizer_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {f : X ⟶ Z} {g : Y ⟶ Z}
  (t : CategoryTheory.Limits.PullbackCone f g) {W : C} {k l : W ⟶ t.pt},
  CategoryTheory.CategoryStruct.comp k t.fst = CategoryTheory.CategoryStruct.comp l t.fst →
    CategoryTheory.CategoryStruct.comp k t.snd = CategoryTheory.CategoryStruct.comp l t.snd →
      ∀ (j : CategoryTheory.Limits.WalkingCospan),
        CategoryTheory.CategoryStruct.comp k (t.π.app j) = CategoryTheory.CategoryStruct.comp l (t.π.app j)

To check whether two morphisms are equalized by the maps of a pullback cone, it suffices to check it for fst t and snd t

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone

Cited by

5 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category