Accessible categories with a class of limits

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139335" target="_blank" >RIV/00216224:14310/24:00139335 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jpaa.2023.107444" target="_blank" >https://doi.org/10.1016/j.jpaa.2023.107444</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2023.107444" target="_blank" >10.1016/j.jpaa.2023.107444</a>

Result language
angličtina
Original language name
Accessible categories with a class of limits
Original language description
In this paper we characterize those accessible V-categories that have limits of a specified class. We do this by introducing the notion of companion C for a class of weights Ψ, as a collection of special types of colimit diagrams that are compatible with Ψ. We then characterize the accessible V-categories with Ψ-limits as those accessibly embedded and C-virtually reflective in a presheaf V-category, and as the V-categories of C-models of sketches. This allows us to recover the standard theorems for locally presentable, locally multipresentable, and locally polypresentable categories as instances of the same general framework. In addition, our theorem covers the case of any weakly sound class Ψ, and provides a new perspective on the case of weakly locally presentable categories.
Czech name
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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
10101 - Pure mathematics

Project
<a href="/en/project/GA22-02964S" target="_blank" >GA22-02964S: Enriched categories and their applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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