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arXiv · 2002.09991

On the tensor product of well generated dg categories

Wendy Lowen·Julia Ramos González
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Abstract

We endow the homotopy category of well generated (pretriangulated) dg categories with a tensor product satisfying a universal property. The resulting monoidal structure is symmetric and closed with respect to the cocontinuous RHom of dg categories (in the sense of To\"en [26]). We give a construction of the tensor product in terms of localisations of dg derived categories, making use of the enhanced derived Gabriel-Popescu theorem [21]. Given a regular cardinal alpha, we define and construct a tensor product of homotopically alpha-cocomplete dg categories and prove that the well generated tensor product of alpha-continuous derived dg categories (in the sense of [21]) is the alpha-continuous dg derived category of the homotopically alpha-cocomplete tensor product. In particular, this shows that the tensor product of well generated dg categories preserves alpha-compactness.

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BibTeXRIS

Wendy Lowen, Julia Ramos González. 2020-02-23. On the tensor product of well generated dg categories. https://doi.org/10.1016/j.jpaa.2021.106843

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