Theorems · Theorem · category theory
CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles
∀ {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],
CategoryTheory.CategoryStruct.comp S.cyclesOpIso.inv S.op.iCycles = S.pOpcycles.op- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- Quiver.Hom.opstatement and proof · cited by 1,948
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.X₂statement and proof · cited by 1,115
- CategoryTheory.Iso.inv_hom_id_assocproof · cited by 275
- CategoryTheory.ShortComplex.cyclesstatement and proof · cited by 220
- CategoryTheory.ShortComplex.opcyclesstatement and proof · cited by 192
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.cyclesOpIso_inv_naturalityproof · cited by 3
- CategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles_assocproof · cited by 1