[Merged by Bors] - feat(LinearAlgebra/PiTensorProduct): some more functoriality properties of PiTensorProduct
#11152
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Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
…ver-community/mathlib4 into SM.PiTensorProduct_functoriality
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…es of `PiTensorProduct` (#11152) * Prove some properties of `PiTensorProduct.map`, for example the compatibility with composition and reindeixing, and the fact that it sends the identity to the identity. * Construct `PiTensorProduct.map` as a `MultilinearMap` on the family of linear maps. * Upgrade `PiTensorProduct.map f` to a linear equivalence called `PiTensorProduct.congr f` when `f` is a family of linear equivalences. * For `ι` a `Fintype`, define the canonical linear equivalence (given by multiplication) `constantBaseRingEquiv` from `⨂ i : ι, R` and `R`. Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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…es of `PiTensorProduct` (#11152) * Prove some properties of `PiTensorProduct.map`, for example the compatibility with composition and reindeixing, and the fact that it sends the identity to the identity. * Construct `PiTensorProduct.map` as a `MultilinearMap` on the family of linear maps. * Upgrade `PiTensorProduct.map f` to a linear equivalence called `PiTensorProduct.congr f` when `f` is a family of linear equivalences. * For `ι` a `Fintype`, define the canonical linear equivalence (given by multiplication) `constantBaseRingEquiv` from `⨂ i : ι, R` and `R`. Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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…es of `PiTensorProduct` (#11152) * Prove some properties of `PiTensorProduct.map`, for example the compatibility with composition and reindeixing, and the fact that it sends the identity to the identity. * Construct `PiTensorProduct.map` as a `MultilinearMap` on the family of linear maps. * Upgrade `PiTensorProduct.map f` to a linear equivalence called `PiTensorProduct.congr f` when `f` is a family of linear equivalences. * For `ι` a `Fintype`, define the canonical linear equivalence (given by multiplication) `constantBaseRingEquiv` from `⨂ i : ι, R` and `R`. Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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…es of `PiTensorProduct` (#11152) * Prove some properties of `PiTensorProduct.map`, for example the compatibility with composition and reindeixing, and the fact that it sends the identity to the identity. * Construct `PiTensorProduct.map` as a `MultilinearMap` on the family of linear maps. * Upgrade `PiTensorProduct.map f` to a linear equivalence called `PiTensorProduct.congr f` when `f` is a family of linear equivalences. * For `ι` a `Fintype`, define the canonical linear equivalence (given by multiplication) `constantBaseRingEquiv` from `⨂ i : ι, R` and `R`. Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Louddy
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…es of `PiTensorProduct` (#11152) * Prove some properties of `PiTensorProduct.map`, for example the compatibility with composition and reindeixing, and the fact that it sends the identity to the identity. * Construct `PiTensorProduct.map` as a `MultilinearMap` on the family of linear maps. * Upgrade `PiTensorProduct.map f` to a linear equivalence called `PiTensorProduct.congr f` when `f` is a family of linear equivalences. * For `ι` a `Fintype`, define the canonical linear equivalence (given by multiplication) `constantBaseRingEquiv` from `⨂ i : ι, R` and `R`. Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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…es of `PiTensorProduct` (#11152) * Prove some properties of `PiTensorProduct.map`, for example the compatibility with composition and reindeixing, and the fact that it sends the identity to the identity. * Construct `PiTensorProduct.map` as a `MultilinearMap` on the family of linear maps. * Upgrade `PiTensorProduct.map f` to a linear equivalence called `PiTensorProduct.congr f` when `f` is a family of linear equivalences. * For `ι` a `Fintype`, define the canonical linear equivalence (given by multiplication) `constantBaseRingEquiv` from `⨂ i : ι, R` and `R`. Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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…es of `PiTensorProduct` (#11152) * Prove some properties of `PiTensorProduct.map`, for example the compatibility with composition and reindeixing, and the fact that it sends the identity to the identity. * Construct `PiTensorProduct.map` as a `MultilinearMap` on the family of linear maps. * Upgrade `PiTensorProduct.map f` to a linear equivalence called `PiTensorProduct.congr f` when `f` is a family of linear equivalences. * For `ι` a `Fintype`, define the canonical linear equivalence (given by multiplication) `constantBaseRingEquiv` from `⨂ i : ι, R` and `R`. Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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PiTensorProduct.map, for example the compatibility with composition and reindeixing, and the fact that it sends the identity to the identity.PiTensorProduct.mapas aMultilinearMapon the family of linear maps.PiTensorProduct.map fto a linear equivalence calledPiTensorProduct.congr fwhenfis a family of linear equivalences.ιaFintype, define the canonical linear equivalence (given by multiplication)constantBaseRingEquivfrom⨂ i : ι, RandR.