2018/02/06 by Moutuou, El-kaïoum M.
#18B40 #18D05 #22A22 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1802.02017
We provide concrete models for generalized morphisms and Morita equivalences of topological 2-groupoids by introducing the notions of crossings and crossed extensions of groupoid crossed modules. A systematic study of these objects is elaborated and an explicit description of how they do yield a groupoid and geometric picture of weak 2-groupoid morphisms is presented. Specifically, we construct a weak 3-category whose objects are crossed modules of topological groupoids and in which weak 1-isomorphisms correspond to Morita equivalences in the "category" of topological 2-groupoids.