local presentability in formal category theory

Has anyone developed a theory of "locally presentable objects" inside a context for formal category theory, such as a Yoneda structure or a proarrow equipment? Hopefully such a theory would specialize both to the classical notion of local presentability, to its enriched version (as developed by Kelly), and to the (infinity,1)-categorical version of Lurie (e.g. using the equipment of quasicategories constructed by Riehl and Verity). Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]