Parametrised Presentability over Orbital Categories
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909059753443328 |
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| author | Hilman, Kaif |
| author_facet | Hilman, Kaif |
| contents | In this paper, we develop the notion of presentability in the parametrised homotopy theory framework of Barwick-Dotto-Glasman-Nardin-Shah over orbital categories. We formulate and prove a characterisation of parametrised presentable categories in terms of its associated straightening. From this we deduce a parametrised adjoint functor theorem from the unparametrised version, prove various localisation results, and we record the interactions of the notion of presentability here with multiplicative matters. Such a theory is of interest for example in equivariant homotopy theory, and we will apply it in a companion work to construct the category of parametrised noncommutative motives for equivariant algebraic K-theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_02594 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Parametrised Presentability over Orbital Categories Hilman, Kaif Algebraic Topology Category Theory K-Theory and Homology 18N60, 55P91 (Primary) In this paper, we develop the notion of presentability in the parametrised homotopy theory framework of Barwick-Dotto-Glasman-Nardin-Shah over orbital categories. We formulate and prove a characterisation of parametrised presentable categories in terms of its associated straightening. From this we deduce a parametrised adjoint functor theorem from the unparametrised version, prove various localisation results, and we record the interactions of the notion of presentability here with multiplicative matters. Such a theory is of interest for example in equivariant homotopy theory, and we will apply it in a companion work to construct the category of parametrised noncommutative motives for equivariant algebraic K-theory. |
| title | Parametrised Presentability over Orbital Categories |
| topic | Algebraic Topology Category Theory K-Theory and Homology 18N60, 55P91 (Primary) |
| url | https://arxiv.org/abs/2202.02594 |