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Theorems · Theorem · category theory

CategoryTheory.ShortComplex.abCyclesIso_inv_apply_iCycles

∀ (S : CategoryTheory.ShortComplex Ab) (x : ↥(AddCommGrpCat.Hom.hom S.g).ker),
  (CategoryTheory.ConcreteCategory.hom S.iCycles) ((CategoryTheory.ConcreteCategory.hom S.abCyclesIso.inv) x) = ↑x
Defined in
Mathlib.Algebra.Homology.ShortComplex.Ab
Cited by
1 results in Mathlib
Foundations
Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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CategoryTheory.ShortComplex.i_cyclesMk · cited by 1ShortComplex.i_cyclesMkDFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homAddSubgroup · cited by 3232AddSubgroupAddMonoidHom · cited by 3230AddMonoidHomCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.X₂ · cited by 1115ShortComplex.X₂CategoryTheory.ShortComplex.X₃ · cited by 876ShortComplex.X₃CategoryTheory.ShortComplex.g · cited by 658ShortComplex.gAddCommGrpCat · cited by 462AddCommGrpCatAddCommGrpCat.carrier · cited by 407AddCommGrpCat.carrierCategoryTheory.ShortComplex.LeftHomologyData.K · cited by 233LeftHomologyData.KCategoryTheory.ShortComplex.cycles · cited by 220ShortComplex.cyclesAb · cited by 198AbShortComplex.abCyclesIso_inv_…CITED BYCITES

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