Taylor Morphisms
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910173448110080 |
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| author | Ng, Gabriel |
| author_facet | Ng, Gabriel |
| contents | We study generalised Taylor morphisms, functors which construct differential ring homomorphisms from ring homomorphisms in a uniform way, analogous to the Taylor expansion for smooth functions. We generalise the construction of the twisted Taylor morphism by León Sánchez and Tressl to arbitrary differential rings by `twisting' the ring of Hurwitz series, and prove that this results in a functor which is the right adjoint to a certain forgetful functor. We therefore give a concrete characterisation of all generalised Taylor morphisms over all differential rings with finitely many commuting derivations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11731 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Taylor Morphisms Ng, Gabriel Commutative Algebra Logic 13N99, 12H05 (Primary), 03C60 (Secondary) We study generalised Taylor morphisms, functors which construct differential ring homomorphisms from ring homomorphisms in a uniform way, analogous to the Taylor expansion for smooth functions. We generalise the construction of the twisted Taylor morphism by León Sánchez and Tressl to arbitrary differential rings by `twisting' the ring of Hurwitz series, and prove that this results in a functor which is the right adjoint to a certain forgetful functor. We therefore give a concrete characterisation of all generalised Taylor morphisms over all differential rings with finitely many commuting derivations. |
| title | Taylor Morphisms |
| topic | Commutative Algebra Logic 13N99, 12H05 (Primary), 03C60 (Secondary) |
| url | https://arxiv.org/abs/2308.11731 |