Two-Vector Spaces and Groupoids

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...

Actions of vector groupoids

In this work we deal with actions of vector groupoid which is a new concept in the literature‎. ‎After we give the definition of the action of a vector groupoid on a vector space‎, ‎we obtain some results related to actions of vector groupoids‎. ‎We also apply some characterizations of the category and groupoid theory to vector groupoids‎. ‎As the second part of the work‎, ‎we define the notion...

Groupoids in Algebraic Spaces

Groupoids in Algebraic Spaces

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...