## Equivalent characterizations of accessible V-categories (part 2)

### Giacomo Tendas – 1 April 2020

In Part 1 we saw how locally presentable categories can be characterised using limit sketches, orthogonality conditions, and reflective subcategories. The aim of this talk is to describe how things change when we talk about accessible categories (i.e. if we drop cocompleteness).

It is known that, in the accessible context, limit sketches correspond to limit/colimits sketches (this is due to Lair and Makkai-Pare'), but what happens to the orthogonality and reflectivity conditions? We'll see that they can be replaced by the two notions of "virtual orthogonality" and "virtual reflectivit" which we'll be introduced during the talk.

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