Groupoids and cogroupoids: an one object approach
arXiv:1207.3694
Abstract
The aim of this paper is to provide a definition of groupoid and cogroupoid internal to a category which makes use of only one object and morphisms, in contrast with the two object approach commonly found in the literature. We will give some examples and we will establish a relation with group objects (and Hopf algebras). The definitions presented here were designed to simplify some constructions related to internalizations, Lie groupoids and Hopf algebroids.
25 pages, no figures. The text was reformulated to eliminate a few unnecessary hypothesis and to improve compatibility with the traditional literature. A few more examples were added and a wrong remark about connections on Lie groupoids was removed