Accessible categories with a class of limits

Stephen Lack, Giacomo Tendas*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Article number107444
Pages (from-to)1-43
Number of pages43
JournalJournal of Pure and Applied Algebra
Issue number2
Publication statusPublished - Feb 2024


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