we give the concept of ‘braiding’ for 2-groupoids, and we show that this structure is equivalent tobraided regular, crossed modules.

The purpose of this paper is to describe orbifolds in terms of (a certain kind of) groupoids. In doing so, I hope to convince you that the theory of (Lie) groupoids provides a most convenient language for developing the foundations of the theory of orbifolds. Indeed, rather than defining all kinds of structures and invariants in a seemingly ad hoc way, often in terms of local charts, one can us...

This work considers concurrent programs formed of processes connected by an underlying network. The symmetries of the network may be used to reduce the state space of the program, by grouping together similar global states. This can result in an exponential reduction for highly symmetric networks, but it is much less effective for many networks, such as rings, which have limited global symmetry...

Hrushovski's suggestion, given in ["Groupoids, imaginaries and internal covers," Turkish Journal of Mathematics , 2012], to capture the structure 1-analysable covers a theory T using simplicial groupoids definable is realized here. The ideas Haykazyan Moosa, found ["Functoriality uniformity groupoid-cover correspondence," Annals Pure Applied Logic 2018] are used, extended, define an equivalence...

Abstract VB-groupoids are vector bundles in the category of Lie groupoids. They encompass several classical objects, including group representations and 2-vector spaces. Moreover, they provide geometric pictures for 2-term up to homotopy We attach every VB-groupoid a cochain complex controlling its deformations discuss fundamental features, such as Morita invariance van Est theorem. Several exa...