Theorems · Theorem · category theory

CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc

∀ {R : Type u} [inst : Ring R] (S : CategoryTheory.ShortComplex (ModuleCat R)) {Z : ModuleCat R}
  (h : S.moduleCatLeftHomologyData.K ⟶ Z),
  CategoryTheory.CategoryStruct.comp S.toCycles (CategoryTheory.CategoryStruct.comp S.moduleCatCyclesIso.hom h) =
    CategoryTheory.CategoryStruct.comp S.moduleCatLeftHomologyData.f' h

Defined in: Mathlib.Algebra.Homology.ShortComplex.ModuleCat
Cited by: 1 results in Mathlib
Foundations: Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring

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Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Iso.homstatement and proof · cited by 7,684
Ringstatement and proof · cited by 7,463
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.ShortComplexstatement and proof · cited by 1,850
ModuleCatstatement and proof · cited by 1,429
CategoryTheory.ShortComplex.X₁statement · cited by 889
CategoryTheory.ShortComplex.LeftHomologyData.Kstatement and proof · cited by 233
CategoryTheory.ShortComplex.cyclesstatement · cited by 220
CategoryTheory.ShortComplex.moduleCatLeftHomologyDatastatement and proof · cited by 106
CategoryTheory.ShortComplex.LeftHomologyData.f'statement and proof · cited by 61

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_applyproof · cited by 0