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arXiv · 2308.11731

Taylor Morphisms

Gabriel Ng
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Abstract

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 Le\'on S\'anchez 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.

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Gabriel Ng. 2023-08-22. Taylor Morphisms. https://doi.org/10.1016/j.jalgebra.2026.04.028

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