Diffeological Coarse Moduli Spaces of Stacks over Manifolds

• DOI: 10.48550/arxiv.1406.1392
• Publication Date: 2014-01-01
• Authors: Jordan Watts; Seth Wolbert
• Keywords: Differential topology

In this paper, we consider diffeological spaces as stacks over the site of smooth manifolds, well "underlying" space any stack. More precisely, so-called concrete sheaves and show that Grothendieck construction sending these to has a left adjoint: functor stack its coarse moduli space. As an application, restrict our attention differentiable examine geometry behind in terms Lie groupoids their principal bundles. Within context, define "gerbe", when groupoid is such gerbe (or represented by one). Additionally, basic differential forms for confirm case agree (under certain conditions) with on representative groupoid. These turn match orbit