Suppose $R$ is a category and $F:R\to Cat$ is a functor (or pseudofunctor). The *oplax limit* of $F$ is the category whose objects consist of an object $x_r \in F(r)$ for all $r$ together with a morphism $x_s \to F(d)(x_{r})$ for all morphisms $d:r\to s$ in $R$, satisfying obvious compatibility conditions.

I have some vague memory of reading a paper in which, given a functor as above in which $R$ is a Reedy category, each category $F(r)$ is a model category, and probably some other conditions, a "Reedy-type" model structure on the oplax limit (or perhaps some related category) was constructed. However, I have been totally unable to find this paper again; the closest I can find is this paper which considers "injective-type" model structures on lax limits. Can anyone point me to the paper I am thinking of?

(I am not interested in seeing proofs or "it seems like this should work" arguments written out in the answers. I only want the reference.)

from$F(r)$to$F(s)$, while $x_s$ is an object in $F(s)$? $\endgroup$ – Jason Gross Jul 30 '13 at 18:04