Two-Vector Spaces and Groupoids |
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Authors: | Jeffrey Colin Morton |
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Affiliation: | 1.Department of Mathematics,University of Western Ontario,London,Canada |
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Abstract: | This paper describes a relationship between essentially finite groupoids and two-vector spaces. In particular, we show to construct two-vector spaces of Vect-valued presheaves on such groupoids. We define two-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—from Span(FinGpd) (the bicategory of essentially finite groupoids and spans of groupoids) into 2Vect. In this paper we prove this and give the construction in detail. |
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