Theorems · Theorem · category theory
CategoryTheory.ShortComplex.RightHomologyData.opcyclesIso_inv_comp_descOpcycles_assoc
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S : CategoryTheory.ShortComplex C} (h : S.RightHomologyData) {A : C} (k : S.X₂ ⟶ A)
(hk : CategoryTheory.CategoryStruct.comp S.f k = 0) [inst_2 : S.HasRightHomology] {Z : C} (h_1 : A ⟶ Z),
CategoryTheory.CategoryStruct.comp h.opcyclesIso.inv (CategoryTheory.CategoryStruct.comp (S.descOpcycles k hk) h_1) =
CategoryTheory.CategoryStruct.comp (h.descQ k hk) h_1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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 and proof · cited by 17,999
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.X₂statement and proof · cited by 1,115
- CategoryTheory.ShortComplex.X₁statement · cited by 889
- CategoryTheory.ShortComplex.fstatement and proof · cited by 653
- CategoryTheory.ShortComplex.RightHomologyDatastatement and proof · cited by 211
- CategoryTheory.ShortComplex.opcyclesstatement · cited by 192
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