Theorems · Theorem · category theory
CategoryTheory.ShortComplex.liftCycles.congr_simp
∀ {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 k_1 : A ⟶ S.X₂) (e_k : k = k_1)
(hk : CategoryTheory.CategoryStruct.comp k S.g = 0) [inst_2 : S.HasLeftHomology],
S.liftCycles k hk = S.liftCycles k_1 ⋯- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.X₃statement · cited by 876
- CategoryTheory.ShortComplex.gstatement and proof · cited by 658
- CategoryTheory.ShortComplex.cyclesstatement · cited by 220
- CategoryTheory.ShortComplex.HasLeftHomologystatement and proof · cited by 132
- CategoryTheory.ShortComplex.liftCyclesstatement and proof · cited by 32
Cited by2
Results whose statement or proof uses this declaration.
- CochainComplex.liftCycles_shift_homologyπproof · cited by 1
- SSet.liftCycles_ιChainComplex_homologyπ_homology₀Iso_homproof · cited by 1