Theorems · Theorem · category theory

CategoryTheory.Limits.biprod.mapBiprod_inv_map_desc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D]
  (F : CategoryTheory.Functor C D) [inst_4 : F.PreservesZeroMorphisms] (X Y : C)
  [inst_5 : CategoryTheory.Limits.HasBinaryBiproduct X Y]
  [inst_6 : CategoryTheory.Limits.PreservesBinaryBiproduct X Y F] {W : C} (f : X ⟶ W) (g : Y ⟶ W),
  CategoryTheory.CategoryStruct.comp (F.mapBiprod X Y).inv (F.map (CategoryTheory.Limits.biprod.desc f g)) =
    CategoryTheory.Limits.biprod.desc (F.map f) (F.map g)

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Limits.HasBinaryBiproductCategoryTheory.Limits.PreservesBinaryBiproduct