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Two-Vector Spaces and Groupoids

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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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  1. Department of Mathematics, University of Western Ontario, London, ON, Canada

    Jeffrey Colin Morton

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  1. Jeffrey Colin Morton
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Correspondence to Jeffrey Colin Morton.

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Morton, J.C. Two-Vector Spaces and Groupoids. Appl Categor Struct 19, 659–707 (2011). https://doi.org/10.1007/s10485-010-9225-0

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  • DOI: https://doi.org/10.1007/s10485-010-9225-0

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