Theorems · Theorem · category theory

CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op

∀ {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],
  CategoryTheory.CategoryStruct.comp S.opcyclesOpIso.hom S.toCycles.op = S.op.fromOpcycles

Defined in: Mathlib.Algebra.Homology.ShortComplex.RightHomology
Cited by: 2 results in Mathlib
Foundations: Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.ShortComplex.HasLeftHomology

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Cites33

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.homstatement and proof · cited by 7,684
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.X₂proof · cited by 1,115
CategoryTheory.ShortComplex.X₁statement and proof · cited by 889
CategoryTheory.ShortComplex.X₃proof · cited by 876
CategoryTheory.ShortComplex.gproof · cited by 658

Cited by2

Results whose statement or proof uses this declaration.

HomologicalComplex.opcyclesOpIso_hom_toCycles_opproof · cited by 2
CategoryTheory.ShortComplex.opcyclesOpIso_hom_toCycles_op_assocproof · cited by 0