2007/08/20 by Hollander, Sharon
#14A20 (Secondary) #18G55 #55U10 (Primary) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.0708.2705
We extend the notion of algebraic stack to an arbitrary subcanonical site C. If the topology on C is local on the target and satisfies descent for morphisms, we show that algebraic stacks are precisely those which are weakly equivalent to representable presheaves of groupoids whose domain map is a cover. This leads naturally to a definition of algebraic n-stacks. We also compare different sites naturally associated to a stack.