[Merged by Bors] - feat(RepresentationTheory/Homological/GroupHomology/Functoriality): low degree functoriality maps#25939
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…ow degree functoriality maps (#25939) Given a commutative ring `k`, a group homomorphism `f : G →* H`, a `k`-linear `G`-representation `A`, a `k`-linear `H`-representation `B`, and a representation morphism `A ⟶ Res(f)(B)`, we get a chain map `inhomogeneousChains A ⟶ inhomogeneousChains B` and hence maps on cohomology `Hₙ(G, A) ⟶ Hₙ(H, B)`. This PR provides specialised API for these maps in low degree. A future PR will add support for switching resolution. Co-authored-by: 101damnations <101damnations@github.com>
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…ow degree functoriality maps (leanprover-community#25939) Given a commutative ring `k`, a group homomorphism `f : G →* H`, a `k`-linear `G`-representation `A`, a `k`-linear `H`-representation `B`, and a representation morphism `A ⟶ Res(f)(B)`, we get a chain map `inhomogeneousChains A ⟶ inhomogeneousChains B` and hence maps on cohomology `Hₙ(G, A) ⟶ Hₙ(H, B)`. This PR provides specialised API for these maps in low degree. A future PR will add support for switching resolution. Co-authored-by: 101damnations <101damnations@github.com>
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…ow degree functoriality maps (leanprover-community#25939) Given a commutative ring `k`, a group homomorphism `f : G →* H`, a `k`-linear `G`-representation `A`, a `k`-linear `H`-representation `B`, and a representation morphism `A ⟶ Res(f)(B)`, we get a chain map `inhomogeneousChains A ⟶ inhomogeneousChains B` and hence maps on cohomology `Hₙ(G, A) ⟶ Hₙ(H, B)`. This PR provides specialised API for these maps in low degree. A future PR will add support for switching resolution. Co-authored-by: 101damnations <101damnations@github.com>
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Given a commutative ring
k, a group homomorphismf : G →* H, ak-linearG-representationA, ak-linearH-representationB, and a representation morphismA ⟶ Res(f)(B), we get a chain mapinhomogeneousChains A ⟶ inhomogeneousChains Band hence maps on cohomologyHₙ(G, A) ⟶ Hₙ(H, B).This PR provides specialised API for these maps in low degree. A future PR will add support for switching resolution.
Action.rhoaMonoidHominstead of a morphism inMonCat#21652Finsupp#21732Rep.diagonal k G (n + 1) ≅ Rep.free k G (Fin n → G)#21736IsCycle₁predicate and friends #25884cycles A nwithcyclesₙ Aforn = 0, 1, 2#25888H0, H1, H2#25908Earlier version at #21763