Theorems · Theorem · category theory

CategoryTheory.ShortComplex.RightHomologyData.exact_map_iff

∀ {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} (h : S.RightHomologyData)
  (F : CategoryTheory.Functor C D) [inst_4 : F.PreservesZeroMorphisms] [h.IsPreservedBy F] [(S.map F).HasHomology],
  (S.map F).Exact ↔ CategoryTheory.Limits.IsZero (F.obj h.H)

Defined in

Mathlib.Algebra.Homology.ShortComplex.Exact

Cited by

1 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.ShortComplex.RightHomologyData.IsPreservedByCategoryTheory.ShortComplex.HasHomology