[Merged by Bors] - feat: basic definitions for Algebra.Homology.ShortComplex.Homology #4204
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…4204) This PR introduces the basic definition of a `HomologyData` for `S : ShortComplex C`.
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…eanprover-community#4204) This PR introduces the basic definition of a `HomologyData` for `S : ShortComplex C`.
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This PR introduces the basic definition of a
HomologyDataforS : ShortComplex C.In future PR, the API shall be developed, and
S.homology : Cshall be defined ash.left.Hfor some choice ofh : S.HomologyData. Then, almost by definition, the homology shall be a self-dual notion.Note: When we know that a short complex
Shas homology (e.g. ifCis abelian), then anyh : S.LeftHomologyDatawill provide an isomorphism
h.homologyIso : S.homology ≅ h.H(and similarly forRightHomologyData). The user may provide bothLeftandRighthomology data, but only one of these shall be necessary.