Theorems · Theorem · category theory

CategoryTheory.Functor.zero_of_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) [F.PreservesZeroMorphisms] [F.Faithful] {X Y : C} (f : X ⟶ Y), F.map f = 0 → f = 0

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero

Cited by

2 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.Faithful