[Merged by Bors] - refactor(RepresentationTheory/GroupCohomology): refactor low degree group cohomology#25870
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PR summary 6213db6954Import changes for modified filesNo significant changes to the import graph Import changes for all files
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…roup cohomology (#25870) `groupCohomology A n` is defined as the abstract homology of the complex of inhomogeneous cochains in `RepresentationTheory.GroupCohomology.Basic`, whose objects are `(Fin n → G) → A`, whilst in `RepresentationTheory.GroupCohomology.LowDegree` we provide alternative definitions of `H0, H1, H2` which are more concrete. But these extra definitions are not worth the extra API they necessitate, as long as we define the (one/two)-co(cycles/boundaries) as submodules of `G → A` and `G × G → A` respectively and relate these (and `Aᴳ`) to the original `groupCohomology A n` for `n = 0, 1, 2`. This PR implements that.
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…roup cohomology (leanprover-community#25870) `groupCohomology A n` is defined as the abstract homology of the complex of inhomogeneous cochains in `RepresentationTheory.GroupCohomology.Basic`, whose objects are `(Fin n → G) → A`, whilst in `RepresentationTheory.GroupCohomology.LowDegree` we provide alternative definitions of `H0, H1, H2` which are more concrete. But these extra definitions are not worth the extra API they necessitate, as long as we define the (one/two)-co(cycles/boundaries) as submodules of `G → A` and `G × G → A` respectively and relate these (and `Aᴳ`) to the original `groupCohomology A n` for `n = 0, 1, 2`. This PR implements that.
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…roup cohomology (leanprover-community#25870) `groupCohomology A n` is defined as the abstract homology of the complex of inhomogeneous cochains in `RepresentationTheory.GroupCohomology.Basic`, whose objects are `(Fin n → G) → A`, whilst in `RepresentationTheory.GroupCohomology.LowDegree` we provide alternative definitions of `H0, H1, H2` which are more concrete. But these extra definitions are not worth the extra API they necessitate, as long as we define the (one/two)-co(cycles/boundaries) as submodules of `G → A` and `G × G → A` respectively and relate these (and `Aᴳ`) to the original `groupCohomology A n` for `n = 0, 1, 2`. This PR implements that.
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groupCohomology A nis defined as the abstract homology of the complex of inhomogeneous cochains inRepresentationTheory.GroupCohomology.Basic, whose objects are(Fin n → G) → A, whilst inRepresentationTheory.GroupCohomology.LowDegreewe provide alternative definitions ofH0, H1, H2which are more concrete. But these extra definitions are not worth the extra API they necessitate, as long as we define the (one/two)-co(cycles/boundaries) as submodules ofG → AandG × G → Arespectively and relate these (andAᴳ) to the originalgroupCohomology A nforn = 0, 1, 2. This PR implements that.This PR continues the work from #25310.
Original PR: #25310