[Merged by Bors] - refactor: introduce the new homology API for homological complex and rename the old one #7954
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Co-authored-by: Johan Commelin <johan@commelin.net>
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…rename the old one (#7954) This PR renames definitions of the current homology API (adding a `'` to `homology`, `cycles`, `QuasiIso`) so as to create space for the development of the new homology API of homological complexes: this PR also contains the new definition of `HomologicalComplex.homology` which involves the homology theory of short complexes. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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…rename the old one (#7954) This PR renames definitions of the current homology API (adding a `'` to `homology`, `cycles`, `QuasiIso`) so as to create space for the development of the new homology API of homological complexes: this PR also contains the new definition of `HomologicalComplex.homology` which involves the homology theory of short complexes. Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>
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This PR renames definitions of the current homology API (adding a
'tohomology,cycles,QuasiIso) so as to create space for the development of the new homology API of homological complexes: this PR also contains the new definition ofHomologicalComplex.homologywhich involves the homology theory of short complexes.Next, the plan is to develop this new homology API, and then make small PRs which remove the downstream uses of the old homology API, replacing these with the new API. Significant steps will include refactors of projective/injective resolutions and left/right derived functors. Enabling the use of the new homology API in the development of group cohomology is also important. (Eventually, when the old API is no longer used and when old statements all have equivalents in the new homology API, it could be removed.)