Theorems · Theorem · category theory

CategoryTheory.Limits.pullbackComparison_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {E : Type u_1} [inst_2 : CategoryTheory.Category.{v_1, u_1} E] (F : CategoryTheory.Functor C D)
  (G : CategoryTheory.Functor D E) {X Y S : C} (f : X ⟶ S) (g : Y ⟶ S) [inst_3 : CategoryTheory.Limits.HasPullback f g]
  [inst_4 : CategoryTheory.Limits.HasPullback (F.map f) (F.map g)]
  [inst_5 : CategoryTheory.Limits.HasPullback (G.map (F.map f)) (G.map (F.map g))]
  [inst_6 : CategoryTheory.Limits.HasPullback ((F.comp G).map f) ((F.comp G).map g)],
  CategoryTheory.Limits.pullbackComparison (F.comp G) f g =
    CategoryTheory.CategoryStruct.comp (G.map (CategoryTheory.Limits.pullbackComparison F f g))
      (CategoryTheory.Limits.pullbackComparison G (F.map f) (F.map g))

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

1 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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