Description:

Title: A category of elements for enriched functors

Abstract: The category of elements (a discrete version of the Grothendieck construction) gives an equivalence between the categories of functors from a fixed category C to Set, and of discrete fibrations over C. It is intimately linked with the study of representable functors, as a well-known result shows that a functor is representable if and only if its category of elements has a terminal object. Hence, the category of elements gives us a way to characterize representable functors, and through them, universal properties, which are then used to understand key constructions such as adjunctions and (co)limits.

In this talk we will introduce a category of elements for enriched functors, and explain how this enjoys all of the desired (enriched) categorical properties. This is based on joint work with Lyne Moser and Paula Verdugo.