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Abstract
The importance of accessible categories has been widely recognized; they can be described as those freely generated in some precise sense by a small set of objects and, because of that, satisfy many good properties. More specifically finitely accessible categories can be characterized as: (a) free cocompletions of small categories under filtered colimits, and (b) categories of flat presheaves on some small category. The equivalence between (a) and (b) is what makes the theory so general and fruitful. Notions of enriched accessibility have also been considered in the literature for various bases of enrichment, such as Ab,SSet,Cat and Met. The problem in this context is that the equivalence between (a) and (b) is no longer true in general. The aim of this paper is then to: 1. give sufficient conditions on V so that (a) ⇔ (b) holds; 2. give sufficient conditions on V so that (a) ⇔ (b) holds up to Cauchy completion; 3. explore some examples not covered by (1) or (2).
Original language  English 

Article number  108381 
Pages (fromto)  150 
Number of pages  50 
Journal  Advances in Mathematics 
Volume  404 
Issue number  Part A 
DOIs  
Publication status  Published  6 Aug 2022 
Keywords
 2category
 Accessible category
 Enriched category
 Filtered colimit
 Flat functor
 Simplicial category
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Dive into the research topics of 'Flat vs. filtered colimits in the enriched context'. Together they form a unique fingerprint.Projects
 1 Finished

Working synthetically in higher categorical structures
Lack, S., Verity, D., Garner, R. & Street, R.
19/06/19 → 18/06/22
Project: Other