Adjoint functor theorems for homotopically enriched categories

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00130448" target="_blank" >RIV/00216224:14310/23:00130448 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0001870822006296" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0001870822006296</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2022.108812" target="_blank" >10.1016/j.aim.2022.108812</a>

Result language
angličtina
Original language name
Adjoint functor theorems for homotopically enriched categories
Original language 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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10100 - Mathematics

Project
<a href="/en/project/GA19-00902S" target="_blank" >GA19-00902S: Injectivity and Monads in Algebra and Topology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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