Limits indexed by category-valued 2-functors

There is common agreement now on the correct general notion of limit for categories whose horns are enriched in a suitable category 13. The definition involves a v-functor J: A + v which should be thought of as a v-diagram scheme; for simplicity, we shall suppose %q is complete enough so that the category of v-valued %functors on OQ admits its natural enrichment to aC13 -category [ 94;,33 1. A J-indexed limit for a %functor S: d + 3c is then an object lim (J, S) of % together with a c13 -natural isomorphism