Theorems · Theorem · category theory

CategoryTheory.Limits.IsZero.map

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
  [CategoryTheory.Limits.HasZeroObject D] [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D]
  {F : CategoryTheory.Functor C D}, CategoryTheory.Limits.IsZero F → ∀ {X Y : C} (f : X ⟶ Y), F.map f = 0

Defined in

Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms

Cited by

1 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms