Lax limits of model categories

Yonatan Harpaz (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

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 $\infty$-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.

Domaines: Mathématiques [math]; Topologie algébrique [math.AT]

Yonatan Harpaz. Lax limits of model categories. Theory and Applications of Categories, 2020, 35, pp.959-978. ⟨hal-02409050⟩