Given a limit sketch in which the cones have a finite connected base, we show that a model structure of “up to homotopy” models for this limit sketch in a suitable model category can be transferred to a Quillen-equivalent model structure on the category of strict models. As a corollary of our general result, we obtain a rigidification theorem which asserts in particular that any –space in the sense of Rezk is levelwise equivalent to one that satisfies the Segal conditions on the nose. There are similar results for dendroidal spaces and –fold Segal spaces.
"Rigidification of higher categorical structures." Algebr. Geom. Topol. 16 (6) 3533 - 3562, 2016. https://doi.org/10.2140/agt.2016.16.3533