Theorems · Theorem · category theory

CategoryTheory.Functor.mapBiproduct_inv

∀ {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] {J : Type w₁}
  (F : CategoryTheory.Functor C D) (f : J → C) [inst_4 : CategoryTheory.Limits.HasBiproduct f]
  [inst_5 : F.PreservesZeroMorphisms] [inst_6 : CategoryTheory.Limits.PreservesBiproduct f F],
  (F.mapBiproduct f).inv = CategoryTheory.Limits.biproduct.desc fun j => F.map (CategoryTheory.Limits.biproduct.ι f j)

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts

Cited by

0 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBiproductCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Limits.PreservesBiproduct