Theorems · Theorem · category theory

isoOfQuasiIsoAt_hom_inv_id_assoc

∀ {ι : Type u_1} {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {c : ComplexShape ι} {K L : HomologicalComplex C c} (f : K ⟶ L)
  (i : ι) [inst_2 : K.HasHomology i] [inst_3 : L.HasHomology i] [inst_4 : QuasiIsoAt f i] {Z : C}
  (h : K.homology i ⟶ Z),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.homologyMap f i)
      (CategoryTheory.CategoryStruct.comp (isoOfQuasiIsoAt f i).inv h) =
    h

Defined in

Mathlib.Algebra.Homology.QuasiIso

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomologyHomologicalComplex.HasHomologyQuasiIsoAt