Theorems · Theorem · category theory
isoOfQuasiIsoAt_hom_inv_id
∀ {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],
CategoryTheory.CategoryStruct.comp (HomologicalComplex.homologyMap f i) (isoOfQuasiIsoAt f i).inv =
CategoryTheory.CategoryStruct.id (K.homology i)- Defined in
- Mathlib.Algebra.Homology.QuasiIso
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Iso.invstatement · cited by 6,514
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- CategoryTheory.Iso.hom_inv_idproof · cited by 264
- HomologicalComplex.homologystatement · cited by 209
- HomologicalComplex.homologyMapstatement · cited by 102
Cited by1
Results whose statement or proof uses this declaration.
- isoOfQuasiIsoAt_hom_inv_id_assocproof · cited by 0