coCartesian fibrations and homotopy colimits

TL;DR

This paper demonstrates that the homotopy colimit of a diagram of quasi-categories can be viewed as a localization of Lurie's higher Grothendieck construction, extending classical results to a higher categorical context.

Contribution

It generalizes Thomason's classical result by relating homotopy colimits of quasi-categories to localizations of the higher Grothendieck construction.

Findings

Homotopy colimit of quasi-categories is a localization of Lurie's higher Grothendieck construction.

Generalizes classical Thomason's result to higher categorical setting.

Provides a new perspective on the homotopy type of diagrams in quasi-categories.

Abstract

The main objective of this paper is to show that the homotopy colimit of a diagram of quasi-categories and indexed by a small category is a localization of Lurie's higher Grothendieck construction of the diagram. We thereby generalize Thomason's classical result which states that the homotopy colimit of a diagram of categories has the homotopy type of (the classifying space of) the Grothendieck construction of the diagram of categories.