Theorems · Theorem · category theory

CategoryTheory.Limits.pullbackComparison_comp_snd

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} {D : Type u₂}
  [inst_1 : CategoryTheory.Category.{v₂, u₂} D] (G : CategoryTheory.Functor C D) (f : X ⟶ Z) (g : Y ⟶ Z)
  [inst_2 : CategoryTheory.Limits.HasPullback f g] [inst_3 : CategoryTheory.Limits.HasPullback (G.map f) (G.map g)],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullbackComparison G f g)
      (CategoryTheory.Limits.pullback.snd (G.map f) (G.map g)) =
    G.map (CategoryTheory.Limits.pullback.snd f g)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

5 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasPullback