Theorems · Theorem · category theory

CategoryTheory.ShortComplex.mapCyclesIso_hom_iCycles

∀ {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)
  (F : CategoryTheory.Functor C D) [inst_4 : F.PreservesZeroMorphisms] [inst_5 : S.HasLeftHomology]
  [inst_6 : F.PreservesLeftHomologyOf S],
  CategoryTheory.CategoryStruct.comp (S.mapCyclesIso F).hom (F.map S.iCycles) = (S.map F).iCycles

Defined in

Mathlib.Algebra.Homology.ShortComplex.PreservesHomology

Cited by

2 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomologyCategoryTheory.Functor.PreservesLeftHomologyOf