Theorems · Theorem · category theory
CategoryTheory.ShortComplex.cycles_ext
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
(S : CategoryTheory.ShortComplex C) [inst_2 : S.HasLeftHomology] {A : C} (f₁ f₂ : A ⟶ S.cycles),
CategoryTheory.CategoryStruct.comp f₁ S.iCycles = CategoryTheory.CategoryStruct.comp f₂ S.iCycles → f₁ = f₂- Cited by
- 2 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 1,115
- CategoryTheory.ShortComplex.cyclesstatement and proof · cited by 220
- CategoryTheory.ShortComplex.HasLeftHomologystatement and proof · cited by 132
- CategoryTheory.ShortComplex.iCyclesstatement and proof · cited by 100
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.comp_liftCyclesproof · cited by 1
- CategoryTheory.ShortComplex.liftCycles_comp_cyclesMapproof · cited by 1