Theorems · Definition · category theory
CategoryTheory.ShortComplex.isoOpcyclesOfIsColimit
{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] →
{cc : CategoryTheory.Limits.CokernelCofork S.f} → CategoryTheory.Limits.IsColimit cc → (cc.pt ≅ S.opcycles)The isomorphism from the point of a colimit cokernel cofork of S.f to S.opcycles.
- Cited by
- 12 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.
Cites17
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.Isostatement · cited by 3,963
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Limits.Cocone.ptstatement · cited by 1,354
- CategoryTheory.ShortComplex.X₂statement · cited by 1,115
- CategoryTheory.ShortComplex.X₁statement · cited by 889
- CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
- CategoryTheory.Limits.IsColimitstatement and proof · cited by 773
- CategoryTheory.Limits.parallelPairstatement · cited by 766
- CategoryTheory.ShortComplex.fstatement and proof · cited by 653
Cited by14
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoImageproof · cited by 4
- CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_homstatement · cited by 3
- CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_invstatement · cited by 2
- CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_hom_comp_ιstatement and proof · cited by 2
- CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoImage_ιstatement and proof · cited by 2
- CategoryTheory.ShortComplex.π_isoOpcyclesOfIsColimit_hom_assocstatement and proof · cited by 1
- CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_inv_homologyιstatement and proof · cited by 1
- CategoryTheory.ShortComplex.pOpcycles_π_isoOpcyclesOfIsColimit_inv_assocstatement and proof · cited by 0
- CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.g'_eqstatement and proof · cited by 0
- CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.isoHomology_hom_comp_ι_assocstatement and proof · cited by 0