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



Author: Hirokazu Nishimura

Source: https://arxiv.org/







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