Theorems · Theorem · category theory

CategoryTheory.Functor.PreservesZeroMorphisms.map_zero

∀ {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} [self : F.PreservesZeroMorphisms] (X Y : C), F.map 0 = 0

For any pair objects F (0: X ⟶ Y) = (0 : F X ⟶ F Y)

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero

Cited by

1 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.Functor.PreservesZeroMorphisms