  We make use of a higher version of the Yoneda embedding to construct, from a
given quasicategory, a simplicially enriched category, as a subcategory of a
well-behaved simplicial model category, whose simplicial nerve is equivalent to
the former quasicategory. We then show that, when the quasicategory is locally
cartesian closed, it is possible to further endow such a simplicial category
with enough structure for it to provide a model of Martin-L\"of type theory.
This correspondence restricts so that elementary higher topoi are seen to model
homotopy type theory.
