Theorems · Theorem · category theory

CategoryTheory.ShortComplex.exact_map_iff_of_faithful

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D] (S : CategoryTheory.ShortComplex C) [S.HasHomology]
  (F : CategoryTheory.Functor C D) [inst_5 : F.PreservesZeroMorphisms] [F.PreservesLeftHomologyOf S]
  [F.PreservesRightHomologyOf S] [F.Faithful], (S.map F).Exact ↔ S.Exact

Defined in

Mathlib.Algebra.Homology.ShortComplex.Exact

Cited by

3 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasHomologyCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesLeftHomologyOfCategoryTheory.Functor.PreservesRightHomologyOfCategoryTheory.Functor.Faithful