## HOMOTOPY LIMITS FOR 2-CATEGORIES

### BibTeX

@MISC{Gambino_homotopylimits,

author = {Nicola Gambino},

title = {HOMOTOPY LIMITS FOR 2-CATEGORIES},

year = {}

}

### OpenURL

### Abstract

Abstract. We study homotopy limits for 2-categories using the theory of Quillen model categories. In order to do so, we establish the existence of projective and injective model structures on diagram 2-categories. Using this result, we describe the homotopical behaviour not only of conical limits but also of weighted limits for 2-categories. Finally, homotopy limits are related to pseudo-limits. 1. Quillen model structures in 2-category theory The 2-category of groupoids, functors, and natural transformations admits a model structure in which the weak equivalences are the equivalence of categories and the fibrations are the Grothendieck fibrations [1, 5, 13]. Similarly, the 2-category of small categories, functors, and natural transformations admits a model structure in which the weak equivalences are the equivalence of categories and the fibrations are the isofibrations, which are functors satisfying a restricted version of the lifting condition for Grothendieck fibrations which involves only isomorphisms [13, 19]. Steve Lack has vastly