I study some definitions of accessible category (see 1) and the applications of that notions; my question: exist a notion of accessible category in therm of enriched category theory? (in case of exist, what uses have?)
1 Answer
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Yes, there is such a thing. Google for the papers "a theory of enriched sketches" and "enriched accessible categories", both by J. Rosický and others. (btw, it's a duplicate of Enriched locally presentable categories )
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1$\begingroup$ As mentioned in answers to the linked near-duplicate question, another key source is Max Kelly’s 1982 paper Structures defined by finite limits in the enriched context. $\endgroup$ Commented Dec 23, 2017 at 12:03