[Merged by Bors] - feat(linear_algebra/pi_tensor_product): define the tensor product of an indexed family of semimodules #5311
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eric-wieser
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Note that as mentioned on zulip, |
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jcommelin
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#5385 is using |
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Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk>
Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk>
Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk>
Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk>
Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk>
Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk>
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✌️ dupuisf can now approve this pull request. To approve and merge a pull request, simply reply with |
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| section semiring | ||
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| variables {ι : Type*} {R : Type*} [comm_semiring R] | ||
| variables {R' : Type*} [comm_semiring R'] [algebra R' R] |
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Requiring algebra feels quite strict here. Was is_scalar_tower not enough?
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I could probably do it with [semimodule R' R] [is_scalar_tower R' R R], but isn't that just equivalent to algebra anyway?
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Ok, thanks for looking into those simp attributes. bors merge |
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…an indexed family of semimodules (#5311) This PR defines the tensor product of an indexed family `s : ι → Type*` of semimodules over commutative semirings. We denote this space by `⨂[R] i, s i` and define it as `free_add_monoid (R × Π i, s i)` quotiented by the appropriate equivalence relation. The treatment follows very closely that of the binary tensor product in `linear_algebra/tensor_product.lean`. Co-authored-by: Frédéric Dupuis <31101893+dupuisf@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Pull request successfully merged into master. Build succeeded: |
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This PR defines the tensor product of an indexed family
s : ι → Type*of semimodules over commutative semirings. We denote this space by⨂[R] i, s iand define it asfree_add_monoid (R × Π i, s i)quotiented by the appropriate equivalence relation. The treatment follows very closely that of the binary tensor product inlinear_algebra/tensor_product.lean.Zulip thread