Theorems · Theorem · category theory

CategoryTheory.Limits.PreservesPullback.iso_hom_fst_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  (G : CategoryTheory.Functor C D) {X Y Z : C} (f : X ⟶ Z) (g : Y ⟶ Z)
  [inst_2 : CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.cospan f g) G]
  [inst_3 : CategoryTheory.Limits.HasPullback f g] [inst_4 : CategoryTheory.Limits.HasPullback (G.map f) (G.map g)]
  {Z_1 : D} (h : G.obj X ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.PreservesPullback.iso G f g).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst (G.map f) (G.map g)) h) =
    CategoryTheory.CategoryStruct.comp (G.map (CategoryTheory.Limits.pullback.fst f g)) h

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks

Cited by

0 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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