Homogeneous spaces of Dirac groupoids

Groupoids in Algebraic Spaces

Groupoids in Algebraic Spaces

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

2-vector Spaces and Groupoids

This paper describes a relationship between essentially finite groupoids and 2-vector spaces. In particular, we show to construct 2-vector spaces of Vect-valued presheaves on such groupoids. We define 2-linear maps corresponding to functors between groupoids in both a covariant and contravariant way, which are ambidextrous adjoints. This is used to construct a representation— a weak functor—fro...

Higher fundamental groupoids for spaces

Fundamental n-groupoids for a topological space are introduced, by techniques based on Moore paths, similar to those used in [G3] for symmetric simplicial sets. Also the 'directed case' is treated, based on a structure introduced in [G6]: a directed topological space, where privileged directions are assigned and paths need not be reversible; such objects are provided with fundamental n-categori...