## On small accessible V-categories and continuity of accessible functors

### Giacomo Tendas – 29 September 2021

It is well known that a small ordinary category is accessible iff it is Cauchy complete (i.e. idempotents split). In this talk we prove the analogue for enriched categories: a small V-category is accessible iff it is Cauchy complete in the enriched sense. As a corollary of the proof we show that an accessible V-functor out of a locally presentable V-category is continuous iff it preserves gamma-small limits, for a determined cardinal gamma.

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