Publication details

Accessible categories with a class of limits

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LACK Stephen TENDAS Giacomo

Year of publication 2024
Type Article in Periodical
Magazine / Source Journal of Pure and Applied Algebra
MU Faculty or unit

Faculty of Science

Keywords Enriched categories; Accessible and locally presentable categories; Sketches and generalizations
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 ?, as a collection of special types of colimit diagrams that are compatible with ?. We then characterize the accessible V-categories with ?-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 ?, and provides a new perspective on the case of weakly locally presentable categories.
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