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Parametrised Presentability over Orbital Categories - MaRDI portal

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Parametrised Presentability over Orbital Categories

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Publication:6505427

arXiv2202.02594MaRDI QIDQ6505427

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Abstract: 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 the parametrised adjoint functor theorem from the unparametrised version and prove various localisation results. Such a theory is of interest for example in equivariant homotopy theory, and we will apply it in a companion paper to construct the category of parametrised noncommutative motives for equivariant algebraic K-theory.





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