Four Eilenberg-Watts theorems (Arthur Pander Maat)

Orateur :  Arthur Pander Maat

Lieu : salle des Séminaires M3

Résumé : 

The Eilenberg-Watts theorem states that a right-exact, additive functor from one category of ring modules to another must be equivalent to a tensor product with a bimodule. I will discuss existing generalizations of this result to modules over additive categories, and to Hilbert modules over C*-algebras. I then present a novel generalization, to Hilbert modules over C*-categories. I sketch the proof and provide some examples. On the way, we meet enriched versions of the Yoneda lemma, as well as coends and Kan extensions.