Theorems · Theorem · category theory

CategoryTheory.Limits.PreservesBiproduct.preserves

∀ {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 : J → C} {F : CategoryTheory.Functor C D} {inst_4 : F.PreservesZeroMorphisms}
  [self : CategoryTheory.Limits.PreservesBiproduct f F] {b : CategoryTheory.Limits.Bicone f} (a : b.IsBilimit),
  Nonempty (F.mapBicone b).IsBilimit

A functor F preserves biproducts of f if F maps every bilimit bicone over f to a bilimit bicone over F.obj ∘ f.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts

Cited by

0 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Limits.PreservesBiproduct