doctrines

definition: a "doctrine" is a small (weakly) groupoid-enriched category with all finite homotopy-limits.

first of all, to what extent does this definition really make sense? and what about an alternative version using simplicially-enriched categories instead of groupoid-enriched? (does this reveal any problems with the given definition?)

what about interpreting an ordinary finite-limits theory as a doctrine according to this definition?
for example the finite-limits theory of a monoid. does this idea contradict some other idea that we had about categorifying the theorem that says that "the finite-limits theory is formed by the opposite of the finitely-presented models" in a certain context??