Theorems · Theorem · category theory

CategoryTheory.Limits.pullbackProdSndIsoProd_inv_fst_snd

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f : X ⟶ Y) (Z : C)
  [inst_1 : CategoryTheory.Limits.HasBinaryProduct Z Y] [inst_2 : CategoryTheory.Limits.HasBinaryProduct Z X]
  [inst_3 : CategoryTheory.Limits.HasPullback CategoryTheory.Limits.prod.snd f],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullbackProdSndIsoProd f Z).inv
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst CategoryTheory.Limits.prod.snd f)
        CategoryTheory.Limits.prod.snd) =
    CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.prod.snd f

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback

Cited by

1 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasBinaryProductCategoryTheory.Limits.HasBinaryProductCategoryTheory.Limits.HasPullback