Abstract. We introduce the category of set-theoretic representations of a matched pair of groupoids. This is a monoidal category endowed with a monoidal functor fl to the category of quivers over the common base of the groupoids in the matched pair. We study monoidal functors between two such categories of representations which preserve the functor fl. We show that the centralizer of such a mon...

We introduce quasi-symplectic groupoids and explain their relation with momentum map theories. This approach enables us to unify into a single framework various momentum map theories, including ordinary Hamiltonian G-spaces, Lu’s momentum maps of Poisson group actions, and the group-valued momentum maps of Alekseev–Malkin–Meinrenken. More precisely, we carry out the following program: (1) We de...

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

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...