Theorems · Theorem · category theory

HomologicalComplex.restrictionCyclesIso_hom_iCycles

∀ {ι : Type u_1} {ι' : Type u_2} {c : ComplexShape ι} {c' : ComplexShape ι'} {C : Type u_3}
  [inst : CategoryTheory.Category.{v_1, u_3} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  (K : HomologicalComplex C c') (e : c.Embedding c') [inst_2 : e.IsRelIff] (j k : ι) (hk : c.next j = k) {j' k' : ι'}
  (hj' : e.f j = j') (hk' : e.f k = k') (hk'' : c'.next j' = k') [inst_3 : K.HasHomology j']
  [inst_4 : (K.restriction e).HasHomology j],
  CategoryTheory.CategoryStruct.comp (K.restrictionCyclesIso e j k hk hj' hk' hk'').hom (K.iCycles j') =
    CategoryTheory.CategoryStruct.comp ((K.restriction e).iCycles j) (K.restrictionXIso e hj').hom

Defined in

Mathlib.Algebra.Homology.Embedding.RestrictionHomology

Cited by

1 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsComplexShape.Embedding.IsRelIffHomologicalComplex.HasHomologyHomologicalComplex.HasHomology