For a diagram of simplicial combinatorial model categories, we show that the associated lax limit, endowed with the projective model structure, is a presentation of the lax limit of the underlying ∞-categories. Our approach can also allow for the indexing category to be simplicial, as long as the diagram factors through its homotopy category. Analogous results for the associated homotopy limit (and other intermediate limits) directly follow.
Keywords: Lax limit, model categories, strictification
2020 MSC: 18G55, 55U35
Theory and Applications of Categories, Vol. 35, 2020, No. 25, pp 959-978.