2-Vector Spaces and Groupoids

Details 2-Vector Spaces and Groupoids 2-Vector Spaces and Groupoids

2008-10-14

arxiv.org/abs/0810.2361v2

Mathematics

Quantum Algebra

44 pages, 5 figures - v2 adds new theorem, significant changes to proofs, new section

Scientific paper

10.1007/s10485-010-9225-0

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--from Span(Gpd) (the bicategory of groupoids and spans of groupoids) into 2Vect. In this paper we prove this and give the construction in detail.

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