Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Representation theorem for enriched categories

Universal properties play an important role in mathematics, as they allow us to make many constructions such as (co)limits, Kan extensions, adjunctions, etc. In particular, a universal property is formulated by requiring that a certain presheaf is representable. The representation theorem gives a useful characterization of these representable presheaves in terms of terminal objects in their category of elements. Going one dimension up and considering 2-categories, with tslil clingman we show that the straightforward generalization of the representation theorem does not hold in general, but instead one needs to pass to a double categorical setting. In this talk, after reviewing the case of ordinary categories and 2-categories, I will explain how to generalize the representation theorem to the more general framework of V-enriched categories, where V is a cartesian closed category. This is joint work with Maru Sarazola, and Paula Verdugo.