Theorems · Definition · category theory
CategoryTheory.ShortComplex.fromOpcycles
{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.HasRightHomology] → S.opcycles ⟶ S.X₃The canonical map S.opcycles ⟶ X₃.
- Cited by
- 38 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.
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 · cited by 32,603
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.X₃statement · cited by 876
- CategoryTheory.ShortComplex.opcyclesstatement · cited by 192
- CategoryTheory.ShortComplex.HasRightHomologystatement and proof · cited by 125
- CategoryTheory.ShortComplex.rightHomologyDataproof · cited by 64
- CategoryTheory.ShortComplex.RightHomologyData.g'proof · cited by 43
Cited by45
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.exact_of_g_is_cokernelproof · cited by 25
- CategoryTheory.ShortComplex.Exact.gIsCokernelproof · cited by 11
- CategoryTheory.ShortComplex.homologyι_comp_fromOpcyclesstatement and proof · cited by 11
- CategoryTheory.ShortComplex.exact_iff_monoproof · cited by 8
- CategoryTheory.ShortComplex.p_fromOpcyclesstatement · cited by 8
- CategoryTheory.ShortComplex.Exact.epi_fproof · cited by 8
- CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesEIsostatement and proof · cited by 7
- CategoryTheory.ShortComplex.Exact.comp_descToInjectiveproof · cited by 6
- CategoryTheory.ShortComplex.homologyIsKernelstatement · cited by 4
- CategoryTheory.ShortComplex.Exact.descToInjectiveproof · cited by 4
- CategoryTheory.ShortComplex.liftHomologystatement and proof · cited by 3
- CategoryTheory.ShortComplex.exact_iff_mono_fromOpcyclesstatement · cited by 2