I am looking for a reference which discusses the 2-categorical properties of the 2-category $St(C,J)$ of stacks and the stackification $\dashv$ inclusion of presheaves 2-adjunction.

My stacks are indexed categories (not necessarily groupoids). I am for example interested in knowing what kind of 2-limits $St(C,J)$ has. Is $St(C,J)$ 2-(co)complete, what properties do the (co)limits have, etc.? I tried hard to find texts about that, but I wasn't able to find anything useful.

**Edit.** I know that 2-categories of stacks have all homotopy (co)limits. I am interested in stronger (Cat-enriched) limits like flexible limits. I want to know if categories of stacks have them and how they are formed. I can show that St(C,J) has all the flexible Cat-enriched limits which $BiCat(C^{op},Cat)$ admits, so it seems like the only thing missing is a proof that $BiCat(C^{op},Cat)$ has flexible limits. The category $BiCat(C^{op},Cat)$ itself is the category of pseudoalgebras for a 2-monad on $\Pi_{C_0}Cat$. In "Two-dimensional monad theory" the authors claim that any two monad $T $ which satisfies some smallness conditions can be replaced by a 2-monad $ T'$ such that $T'Alg= PsdTAlg$ are Cat-enriched equivalent. This would imply that categories of stacks have all flexible limits. But unfortunately the papers which the authors of "Two-dimensional monad theory" promised never appeard. (I can't find them). So I guess what I am really looking for is a reference for the $T'Alg = PsdTAlg$ result. It is mentioned very often, so I assume some reference must exist. Where can I find it? :)