Virtual concepts in the theory of accessible categories

Stephen Lack, Giacomo Tendas

Research output: Contribution to journalArticlepeer-review


We provide a new characterization of enriched accessible categories by introducing the two new notions of virtual reflectivity and virtual orthogonality as a generalization of the usual reflectivity and orthogonality conditions for locally presentable categories. The word virtual refers to the fact that the reflectivity and orthogonality conditions are given in the free completion of the V-category involved under small limits, instead of the V-category itself. In this way we hope to provide a clearer understanding of the theory as well as a useful way of recognizing accessible V-categories. In the last section we prove that the 2-category of accessible V-categories, accessible V-functors, and V-natural transformations has all flexible limits.

Original languageEnglish
Article number107196
JournalJournal of Pure and Applied Algebra
Issue number2
Early online date21 Jul 2022
Publication statusPublished - 1 Feb 2023


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