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Theorems · Theorem · category theory

CategoryTheory.ShortComplex.exact_iff_surjective_abToCycles

∀ (S : CategoryTheory.ShortComplex Ab), S.Exact ↔ Function.Surjective ⇑S.abToCycles
Defined in
Mathlib.Algebra.Homology.ShortComplex.Ab
Cited by
1 results in Mathlib
Foundations
Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
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CategoryTheory.ShortComplex.ab_exact_iff · cited by 10ShortComplex.ab_exact_iffDFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomAddSubgroup · cited by 3232AddSubgroupAddMonoidHom · cited by 3230AddMonoidHomCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.X₂ · cited by 1115ShortComplex.X₂CategoryTheory.ShortComplex.X₁ · cited by 889ShortComplex.X₁CategoryTheory.ShortComplex.X₃ · cited by 876ShortComplex.X₃CategoryTheory.Epi · cited by 688CategoryTheory.EpiCategoryTheory.ShortComplex.g · cited by 658ShortComplex.gAddCommGrpCat.carrier · cited by 407AddCommGrpCat.carrierCategoryTheory.ShortComplex.Exact · cited by 292ShortComplex.ExactCategoryTheory.ShortComplex.LeftHomologyData.K · cited by 233LeftHomologyData.KAb · cited by 198AbAddMonoidHom.ker · cited by 158AddMonoidHom.kerShortComplex.exact_iff_surjec…CITED BYCITES

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