Compatible tolerances on groupoids

Some Basics on Tolerances

In this paper we deal with sensitivity analysis of combinatorial optimization problems and its fundamental term, the tolerance. For three classes of objective functions (Σ,Π,MAX) we give some basic properties on upper and lower tolerances. We show that the upper tolerance of an element is well defined, how to compute the upper tolerance of an element, and give equivalent formulations when the u...

On Groupoids and Hypergraphs

We present a novel construction of finite groupoids whose Cayley graphs have large girth even w.r.t. a discounted distance measure that contracts arbitrarily long sequences of edges from the same colour class (subgroupoid), and only counts transitions between colour classes (cosets). These groupoids are employed towards a generic construction method for finite hypergraphs that realise specified...

On Braided Groupoids

We study and give examples of braided groupoids, and a fortiori, non-degenerate solutions of the quiver-theoretical braid equation.

n-groupoids and stacky groupoids

We discuss two generalizations of Lie groupoids. One consists of Lie n-groupoids defined as simplicial manifolds with trivial πk≥n+1. The other consists of stacky Lie groupoids G ⇒ M with G a differentiable stack. We build a 1–1 correspondence between Lie 2-groupoids and stacky Lie groupoids up to a certain Morita equivalence. We prove this in a general set-up so that the statement is valid in ...

On Ideals of Implication Groupoids