A Functorial Approach to the Infinitesimal Theory of Groupoids

Details A Functorial Approach to the Infinitesimal Theory of Groupoids A Functorial Approach to the Infinitesimal Theory of Groupoids

2007-09-23

arxiv.org/abs/0709.3629v3

Mathematics

Differential Geometry

Scientific paper

Lie algebroids are by no means natural as an infinitesimal counterpart of groupoids. In this paper we propose a functorial construction called Nishimura algebroids for an infinitesimal counterpart of groupoids. Nishimura algebroids, intended for differential geometry, are of the same vein as Lawvere's functorial notion of algebraic theory and Ehresmann's functorial notion of theory called sketches. We study totally intransitive Nishimura algebroids in detail. Finally we show that Nishimura algebroids naturally give rise to Lie algebroids.

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