[Merged by Bors] - feat(RepresentationTheory/Coinvariants): coinvariants of a representation#21733
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101damnations wants to merge 111 commits intomasterfrom
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[Merged by Bors] - feat(RepresentationTheory/Coinvariants): coinvariants of a representation#21733101damnations wants to merge 111 commits intomasterfrom
101damnations wants to merge 111 commits intomasterfrom
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| variable (k G) | ||
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| /-- The functor sending a representation to its coinvariants. -/ | ||
| @[simps obj map] |
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This should be unsimped if the normal form is now functor.obj _.
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Thanks, I've tried changing the simps to obj_carrier and map_hom
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Thanks! bors merge |
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…tion (#21733) Given a commutative ring `k` and a monoid `G`, this PR introduces the coinvariants of a `k`-linear `G`-representation `(V, ρ)`. We first define `Representation.Coinvariants.ker`, the submodule of `V` generated by elements of the form `ρ g x - x` for `x : V`, `g : G`. Then the coinvariants of `(V, ρ)` are the quotient of `V` by this submodule. We show that the functor sending a representation to its coinvariants is left adjoint to the functor equipping a module with the trivial representation. Co-authored-by: 101damnations <al3717@ic.ac.uk>
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…tion (leanprover-community#21733) Given a commutative ring `k` and a monoid `G`, this PR introduces the coinvariants of a `k`-linear `G`-representation `(V, ρ)`. We first define `Representation.Coinvariants.ker`, the submodule of `V` generated by elements of the form `ρ g x - x` for `x : V`, `g : G`. Then the coinvariants of `(V, ρ)` are the quotient of `V` by this submodule. We show that the functor sending a representation to its coinvariants is left adjoint to the functor equipping a module with the trivial representation. Co-authored-by: 101damnations <al3717@ic.ac.uk>
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…tion (#21733) Given a commutative ring `k` and a monoid `G`, this PR introduces the coinvariants of a `k`-linear `G`-representation `(V, ρ)`. We first define `Representation.Coinvariants.ker`, the submodule of `V` generated by elements of the form `ρ g x - x` for `x : V`, `g : G`. Then the coinvariants of `(V, ρ)` are the quotient of `V` by this submodule. We show that the functor sending a representation to its coinvariants is left adjoint to the functor equipping a module with the trivial representation. Co-authored-by: 101damnations <al3717@ic.ac.uk>
TOMILO87
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…tion (#21733) Given a commutative ring `k` and a monoid `G`, this PR introduces the coinvariants of a `k`-linear `G`-representation `(V, ρ)`. We first define `Representation.Coinvariants.ker`, the submodule of `V` generated by elements of the form `ρ g x - x` for `x : V`, `g : G`. Then the coinvariants of `(V, ρ)` are the quotient of `V` by this submodule. We show that the functor sending a representation to its coinvariants is left adjoint to the functor equipping a module with the trivial representation. Co-authored-by: 101damnations <al3717@ic.ac.uk>
This was referenced Jun 14, 2025
[Merged by Bors] - feat(RepresentationTheory/Homological/GroupHomology): long exact sequences
#25943
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callesonne
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…tion (leanprover-community#21733) Given a commutative ring `k` and a monoid `G`, this PR introduces the coinvariants of a `k`-linear `G`-representation `(V, ρ)`. We first define `Representation.Coinvariants.ker`, the submodule of `V` generated by elements of the form `ρ g x - x` for `x : V`, `g : G`. Then the coinvariants of `(V, ρ)` are the quotient of `V` by this submodule. We show that the functor sending a representation to its coinvariants is left adjoint to the functor equipping a module with the trivial representation. Co-authored-by: 101damnations <al3717@ic.ac.uk>
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Given a commutative ring
kand a monoidG, this PR introduces the coinvariants of ak-linearG-representation(V, ρ).We first define
Representation.Coinvariants.ker, the submodule ofVgenerated by elements of the formρ g x - xforx : V,g : G. Then the coinvariants of(V, ρ)are the quotient ofVby this submodule. We show that the functor sending a representation to its coinvariants is left adjoint to the functor equipping a module with the trivial representation.Action.rhoaMonoidHominstead of a morphism inMonCat#21652