Theorems · Theorem · category theory

CategoryTheory.Functor.isZero_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} D]
  [CategoryTheory.Limits.HasZeroObject D] (F : CategoryTheory.Functor C D),
  CategoryTheory.Limits.IsZero F ↔ ∀ (X : C), CategoryTheory.Limits.IsZero (F.obj X)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObject