Theorems · Theorem · category theory

HomologicalComplex.pOpcycles_restrictionOpcyclesIso_hom

∀ {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] (i j : ι) (hi : c.prev j = i) {i' j' : ι'}
  (hi' : e.f i = i') (hj' : e.f j = j') (hi'' : c'.prev j' = i') [inst_3 : K.HasHomology j']
  [inst_4 : (K.restriction e).HasHomology j],
  CategoryTheory.CategoryStruct.comp ((K.restriction e).pOpcycles j)
      (K.restrictionOpcyclesIso e i j hi hi' hj' hi'').hom =
    CategoryTheory.CategoryStruct.comp (K.restrictionXIso e hj').hom (K.pOpcycles j')

Defined in

Mathlib.Algebra.Homology.Embedding.RestrictionHomology

Cited by

3 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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