2-向量空间与群胚
2-Vector Spaces and Groupoids
摘要：
本文描述了本质有限群胚与2-向量空间之间的关系。特别地，我们证明了在这样的群胚上构造2-向量空间的向量值预层。定义了2-线性映射对应于群胚之间函子的协变和逆变形式，它们是模糊伴随的。这是用来构造一个表示-一个弱函子-从Span（Gpd）（群胚和群胚的span的双范畴）到2 Vect。在本文中，我们证明了这一点，并给出了详细的建设。
英文摘要：
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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