Publication details

Adjoint functor theorems for homotopically enriched categories

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BOURKE John Denis LACK Stephen VOKŘÍNEK Lukáš

Year of publication 2023
Type Article in Periodical
Magazine / Source Advances in Mathematics
MU Faculty or unit

Faculty of Science

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Keywords Adjoint functor theorem; Enriched category; Homotopy theory
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Description We prove an adjoint functor theorem in the setting of categories enriched in a monoidal model category admitting certain limits. When is equipped with the trivial model structure this recaptures the enriched version of Freyd's adjoint functor theorem. For non-trivial model structures, we obtain new adjoint functor theorems of a homotopical flavour — in particular, when is the category of simplicial sets we obtain a homotopical adjoint functor theorem appropriate to the ?-cosmoi of Riehl and Verity. We also investigate accessibility in the enriched setting, in particular obtaining homotopical cocompleteness results for accessible ?-cosmoi.
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