Theorems · Theorem · category theory
CategoryTheory.ShortComplex.liftCycles_comp_cyclesMap
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
(S : CategoryTheory.ShortComplex C) {S₁ : CategoryTheory.ShortComplex C} {A : C} (k : A ⟶ S.X₂)
(hk : CategoryTheory.CategoryStruct.comp k S.g = 0) [inst_2 : S.HasLeftHomology] (φ : S ⟶ S₁)
[inst_3 : S₁.HasLeftHomology],
CategoryTheory.CategoryStruct.comp (S.liftCycles k hk) (CategoryTheory.ShortComplex.cyclesMap φ) =
S₁.liftCycles (CategoryTheory.CategoryStruct.comp k φ.τ₂) ⋯- Cited by
- 1 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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.X₃statement · cited by 876
- CategoryTheory.ShortComplex.gstatement and proof · cited by 658
- CategoryTheory.ShortComplex.Hom.τ₂statement and proof · cited by 243
- CategoryTheory.ShortComplex.cyclesstatement · cited by 220
- CategoryTheory.ShortComplex.HasLeftHomologystatement and proof · cited by 132
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.liftCycles_comp_cyclesMap_assocproof · cited by 4