UC Berkeley

In developing homotopy theory in algebraic geometry, Michael Artin and Barry Mazur studied the \'etale homotopy types of schemes. Later, Eric Friedlander generalized them to the \'etale topological types of simplicial schemes. The aim of this paper is to extend further these theories to algebraic stacks. To achieve this goal, we exploit the derived functor approach of \'etale homotopy types by Ilan Barnea and Tomer Schlank, and use Daniel Isaksen's model category structure on pro-simplicial sets.