mathlib3
8c1e2da7 - feat(linear_algebra/tensor_algebra): Tensor algebras (#3531)

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5 years ago
feat(linear_algebra/tensor_algebra): Tensor algebras (#3531) This PR constructs the tensor algebra of a module over a commutative ring. The main components are: 1. The construction of the tensor algebra: `tensor_algebra R M` for a module `M` over a commutative ring `R`. 2. The linear map `univ R M` from `M` to `tensor_algebra R M`. 3. Given a linear map `f`from `M`to an `R`-algebra `A`, the lift of `f` to `tensor_algebra R M` is denoted `lift R M f`. 4. A theorem `univ_comp_lift` asserting that the composition of `univ R M` with `lift R M f`is `f`. 5. A theorem `lift_unique` asserting the uniqueness of `lift R M f`with respect to property 4. Co-authored-by: Adam Topaz <adamtopaz@users.noreply.github.com> Co-authored-by: Patrick Massot <patrickmassot@free.fr>
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