Theorems · Theorem · category theory
CategoryTheory.ShortComplex.opcyclesMap_comp_descOpcycles
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S S₁ : CategoryTheory.ShortComplex C} {A : C} (k : S.X₂ ⟶ A) (hk : CategoryTheory.CategoryStruct.comp S.f k = 0)
[inst_2 : S.HasRightHomology] (φ : S₁ ⟶ S) [inst_3 : S₁.HasRightHomology],
CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.opcyclesMap φ) (S.descOpcycles k hk) =
S₁.descOpcycles (CategoryTheory.CategoryStruct.comp φ.τ₂ k) ⋯- Cited by
- 1 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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.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.cancel_epiproof · cited by 380
- CategoryTheory.ShortComplex.Hom.τ₂statement and proof · cited by 243
- CategoryTheory.ShortComplex.opcyclesstatement and proof · cited by 192
- CategoryTheory.ShortComplex.HasRightHomologystatement and proof · cited by 125
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.opcyclesMap_comp_descOpcycles_assocproof · cited by 0