Theorems · Theorem · category theory

CategoryTheory.Functor.reflects_exact_of_faithful

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Abelian C] {D : Type u₂}
  [inst_2 : CategoryTheory.Category.{v₂, u₂} D] [inst_3 : CategoryTheory.Abelian D] (F : CategoryTheory.Functor C D)
  [inst_4 : F.PreservesZeroMorphisms] [F.Faithful] (S : CategoryTheory.ShortComplex C), (S.map F).Exact → S.Exact

Defined in

Mathlib.CategoryTheory.Abelian.Exact

Cited by

3 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.Faithful