Internal Homs via extensions of dg functors

Abstract

We provide a simple proof of the existence of internal Homs in the localization of the category of dg categories with respect to all quasi-equivalences and of some of their main properties such as the so-called derived Morita theory. This was originally proved in a seminal paper by Toën.

19 pages. Minor changes with respect to the published version: the statement and proof of Proposition 3.10 have been changed and the result is now completed by Corollary 3.13