Theorems · Theorem · category theory

CategoryTheory.Limits.biproduct.map_lift_mapBiprod

∀ {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] {J : Type w₁} (f : J → C)
  [inst_5 : CategoryTheory.Limits.HasBiproduct f] [inst_6 : CategoryTheory.Limits.PreservesBiproduct f F] {W : C}
  (g : (j : J) → W ⟶ f j),
  CategoryTheory.CategoryStruct.comp (F.map (CategoryTheory.Limits.biproduct.lift g)) (F.mapBiproduct f).hom =
    CategoryTheory.Limits.biproduct.lift fun j => F.map (g 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.Functor.PreservesZeroMorphismsCategoryTheory.Limits.HasBiproductCategoryTheory.Limits.PreservesBiproduct