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arXiv · 2111.00147

Accessible $\infty$-cosmoi

John Bourke·Stephen Lack
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Abstract

We introduce the notion of an accessible $\infty$-cosmos and prove that these include the basic examples of $\infty$-cosmoi and are stable under the main constructions. A consequence is that the vast majority of known examples of $\infty$-cosmoi are accessible. By the adjoint functor theorem for homotopically enriched categories which we proved in an earlier paper, joint with Lukas Vokrinek, it follows, for instance, that all such $\infty$-cosmoi have flexibly weighted homotopy colimits.

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John Bourke, Stephen Lack. 2021-10-30. Accessible $\infty$-cosmoi. https://doi.org/10.1016/j.jpaa.2022.107255

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