[Merged by Bors] - feat(RepresentationTheory/*): representations on Finsupp#21732
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101damnations wants to merge 98 commits intomasterfrom
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[Merged by Bors] - feat(RepresentationTheory/*): representations on Finsupp#21732101damnations wants to merge 98 commits intomasterfrom
Finsupp#21732101damnations wants to merge 98 commits intomasterfrom
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Given a type `α` and a representation `A`, this PR defines `Rep.finsupp`, the representation defined pointwise on `α →₀ A`, and specializes this to `Rep.free`, when `A = leftRegular k G`. We define `Rep.freeLiftLEquiv α A`, the `k`-linear equivalence between functions `α → A` and representation morphisms `Rep.free k G α ⟶ A`. We also define representation isomorphisms `(α →₀ A) ⊗ B ≅ (A ⊗ B) →₀ α ≅ A ⊗ (α →₀ B)` given representations `A` and `B`, and finally `k[G] ⊗ (α →₀ k) ≅ free k G α` where `α →₀ k` is equipped with the trivial representation. Co-authored-by: Amelia Livingston <40745104+101damnations@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: 101damnations <al3717@ic.ac.uk>
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Given a type `α` and a representation `A`, this PR defines `Rep.finsupp`, the representation defined pointwise on `α →₀ A`, and specializes this to `Rep.free`, when `A = leftRegular k G`. We define `Rep.freeLiftLEquiv α A`, the `k`-linear equivalence between functions `α → A` and representation morphisms `Rep.free k G α ⟶ A`. We also define representation isomorphisms `(α →₀ A) ⊗ B ≅ (A ⊗ B) →₀ α ≅ A ⊗ (α →₀ B)` given representations `A` and `B`, and finally `k[G] ⊗ (α →₀ k) ≅ free k G α` where `α →₀ k` is equipped with the trivial representation. Co-authored-by: Amelia Livingston <40745104+101damnations@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: 101damnations <al3717@ic.ac.uk>
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…]` to `Finsupp.finsuppProd(L)Equiv` (leanprover-community#23021) This was raised by @Whysoserioushah regarding leanprover-community#21732. We add `Finsupp.uncurry_apply`, which simplifies `Finsupp.uncurry` applied to a term of a product type `xy : α × β`, to prevent `Basis.smulTower_repr` breaking. However, we don't tag this with `@[simp]`; there is already a `@[simp]` tag on the less eager `Finsupp.uncurry_apply_pair`, which applies to a pair of terms `x : α`, `y : β`.
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…r-community#21732) Given a type `α` and a representation `A`, this PR defines `Rep.finsupp`, the representation defined pointwise on `α →₀ A`, and specializes this to `Rep.free`, when `A = leftRegular k G`. We define `Rep.freeLiftLEquiv α A`, the `k`-linear equivalence between functions `α → A` and representation morphisms `Rep.free k G α ⟶ A`. We also define representation isomorphisms `(α →₀ A) ⊗ B ≅ (A ⊗ B) →₀ α ≅ A ⊗ (α →₀ B)` given representations `A` and `B`, and finally `k[G] ⊗ (α →₀ k) ≅ free k G α` where `α →₀ k` is equipped with the trivial representation. Co-authored-by: Amelia Livingston <40745104+101damnations@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: 101damnations <al3717@ic.ac.uk>
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Given a type `α` and a representation `A`, this PR defines `Rep.finsupp`, the representation defined pointwise on `α →₀ A`, and specializes this to `Rep.free`, when `A = leftRegular k G`. We define `Rep.freeLiftLEquiv α A`, the `k`-linear equivalence between functions `α → A` and representation morphisms `Rep.free k G α ⟶ A`. We also define representation isomorphisms `(α →₀ A) ⊗ B ≅ (A ⊗ B) →₀ α ≅ A ⊗ (α →₀ B)` given representations `A` and `B`, and finally `k[G] ⊗ (α →₀ k) ≅ free k G α` where `α →₀ k` is equipped with the trivial representation. Co-authored-by: Amelia Livingston <40745104+101damnations@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: 101damnations <al3717@ic.ac.uk>
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Given a type `α` and a representation `A`, this PR defines `Rep.finsupp`, the representation defined pointwise on `α →₀ A`, and specializes this to `Rep.free`, when `A = leftRegular k G`. We define `Rep.freeLiftLEquiv α A`, the `k`-linear equivalence between functions `α → A` and representation morphisms `Rep.free k G α ⟶ A`. We also define representation isomorphisms `(α →₀ A) ⊗ B ≅ (A ⊗ B) →₀ α ≅ A ⊗ (α →₀ B)` given representations `A` and `B`, and finally `k[G] ⊗ (α →₀ k) ≅ free k G α` where `α →₀ k` is equipped with the trivial representation. Co-authored-by: Amelia Livingston <40745104+101damnations@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: 101damnations <al3717@ic.ac.uk>
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[Merged by Bors] - feat(RepresentationTheory/Homological/GroupHomology): long exact sequences
#25943
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callesonne
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…r-community#21732) Given a type `α` and a representation `A`, this PR defines `Rep.finsupp`, the representation defined pointwise on `α →₀ A`, and specializes this to `Rep.free`, when `A = leftRegular k G`. We define `Rep.freeLiftLEquiv α A`, the `k`-linear equivalence between functions `α → A` and representation morphisms `Rep.free k G α ⟶ A`. We also define representation isomorphisms `(α →₀ A) ⊗ B ≅ (A ⊗ B) →₀ α ≅ A ⊗ (α →₀ B)` given representations `A` and `B`, and finally `k[G] ⊗ (α →₀ k) ≅ free k G α` where `α →₀ k` is equipped with the trivial representation. Co-authored-by: Amelia Livingston <40745104+101damnations@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: 101damnations <al3717@ic.ac.uk>
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Given a type
αand a representationA, this PR definesRep.finsupp, the representation defined pointwise onα →₀ A, and specializes this toRep.free, whenA = leftRegular k G.We define
Rep.freeLiftLEquiv α A, thek-linear equivalence between functionsα → Aand representation morphismsRep.free k G α ⟶ A.We also define representation isomorphisms
(α →₀ A) ⊗ B ≅ (A ⊗ B) →₀ α ≅ A ⊗ (α →₀ B)given representationsAandB, and finallyk[G] ⊗ (α →₀ k) ≅ free k G αwhereα →₀ kis equipped with the trivial representation.Action.rhoaMonoidHominstead of a morphism inMonCat#21652Finsupp.(un)curry_singleand@[simps]toFinsupp.finsuppProd(L)Equiv#23021