Theorems · Theorem · category theory
CategoryTheory.ShortComplex.p_descOpcycles_assoc
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
(S : CategoryTheory.ShortComplex C) {A : C} (k : S.X₂ ⟶ A) (hk : CategoryTheory.CategoryStruct.comp S.f k = 0)
[inst_2 : S.HasRightHomology] {Z : C} (h : A ⟶ Z),
CategoryTheory.CategoryStruct.comp S.pOpcycles (CategoryTheory.CategoryStruct.comp (S.descOpcycles k hk) h) =
CategoryTheory.CategoryStruct.comp k h- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 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 and proof · cited by 17,999
- 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.opcyclesstatement · cited by 192
- CategoryTheory.ShortComplex.HasRightHomologystatement and proof · cited by 125
- CategoryTheory.ShortComplex.pOpcyclesstatement and proof · cited by 84
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.pOpcycles_comp_moduleCatOpcyclesIso_homproof · cited by 2
- CategoryTheory.ShortComplex.descOpcycles_compproof · cited by 1