2023/05/02 by Wolfson, Jesse
#55R10 #55R65 #55R91 #55U10 #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2305.01630
Simplicial objects sC in descent categories C, as introduced by Behrend and Getzler, provide a context in which to study higher stacks. In this note, we extend the construction of the canonical cocycle of a smooth principal G-bundle to the context of principal G-bundles in sC/X. As an application, we show how this specializes to C=Sets to give a streamlined construction of k-invariants of reduced Kan complexes. We adapt this to give a similarly streamlined construction of minimal Kan complexes, with the goal of clarifying the role of the axiom of choice; Postnikov towers of minimal Kan complexes provide examples of towers of simplicial principal bundles of the type we consider.