Okay, so, given an ∞-topos C and X∊C, and another ∞-topos D, is there always some notion of an X-shape inside of D given by taking the colimit of the constant functor C/X→D?

I'm sort of thinking there's something wrong with this... that seems too big?

E.g. C=Top then I'm doing something like taking the colimit of the constant functor over Top/X...

@JonathanBeardsley C/X has a terminal object (id_X : X -> X), so the colimit of a functor F : C/X -> D is just the value of F at (id_X : X -> X).