Theorems · Theorem · category theory

HomologicalComplex.iCyclesIso_inv_hom_id

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {ι : Type u_2} {c : ComplexShape ι} (K : HomologicalComplex C c) (i j : ι) (hj : c.next i = j) (h : K.d i j = 0)
  [inst_2 : K.HasHomology i],
  CategoryTheory.CategoryStruct.comp (K.iCyclesIso i j hj h).inv (K.iCycles i) =
    CategoryTheory.CategoryStruct.id (K.X i)

Defined in

Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomology