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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.09494 |
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| _version_ | 1866917264259809280 |
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| author | Paré, Robert |
| author_facet | Paré, Robert |
| contents | Partial difference operators for a large class of functors between presheaf categories are introduced, extending our difference operator from \cite{Par24} to the multivariable case. These combine into the Jacobian profunctor which provides the setting for a lax chain rule. We introduce a functorial version of multivariable Newton series whose aim is to recover a functor from its iterated differences. Not all functors are recovered but we get a best approximation in the form of a left adjoint, and the induced comonad is idempotent. Its fixed points are what we call soft analytic functors, a generalization of the multivariable analytic functors of Fiore et al.~\cite{FioGamHylWin08}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multivariate functorial difference Paré, Robert Category Theory 18A22, 12H10, 18D60, 18F20, 18F40 (Primary) 18F50 (Secondary) Partial difference operators for a large class of functors between presheaf categories are introduced, extending our difference operator from \cite{Par24} to the multivariable case. These combine into the Jacobian profunctor which provides the setting for a lax chain rule. We introduce a functorial version of multivariable Newton series whose aim is to recover a functor from its iterated differences. Not all functors are recovered but we get a best approximation in the form of a left adjoint, and the induced comonad is idempotent. Its fixed points are what we call soft analytic functors, a generalization of the multivariable analytic functors of Fiore et al.~\cite{FioGamHylWin08}. |
| title | Multivariate functorial difference |
| topic | Category Theory 18A22, 12H10, 18D60, 18F20, 18F40 (Primary) 18F50 (Secondary) |
| url | https://arxiv.org/abs/2409.09494 |