Séminaire Algèbre Géométrie Algébrique Topologie Algébrique :

Le 11 avril 2024 à 10:00 - salle 430

Présentée par Moser Lyne -

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.