Theorems · Theorem · category theory
CategoryTheory.ShortComplex.RightHomologyData.p_descQ
∀ {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), CategoryTheory.CategoryStruct.comp h.p (h.descQ k hk) = k- Cited by
- 8 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.ShortComplex.RightHomologyDatastatement and proof · cited by 211
- CategoryTheory.ShortComplex.RightHomologyData.Qstatement · cited by 163
- CategoryTheory.ShortComplex.RightHomologyData.pstatement · cited by 84
- CategoryTheory.Limits.IsColimit.facproof · cited by 82
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.RightHomologyData.p_g'proof · cited by 17
- CategoryTheory.ShortComplex.p_descOpcyclesproof · cited by 9
- CategoryTheory.ShortComplex.RightHomologyData.p_descQ_assocproof · cited by 2
- CategoryTheory.ShortComplex.RightHomologyData.isIso_pproof · cited by 2
- CategoryTheory.ShortComplex.isIso_opcyclesMap'_of_isIso_of_epiproof · cited by 1
- CategoryTheory.ShortComplex.RightHomologyData.ofIsLimitKernelFork_descQproof · cited by 0