On the monad of internal groupoids

Dominique Bourn

We deeply analyse the structural organisation of the fibration of points and of the monad of internal groupoids. From that we derive: 1) a new characterization of internal groupoids among reflexive graphs in the Mal'cev context; 2) a setting in which a Mal'cev category is necessarily a protomodular category.

Keywords: Fibration of points, monad of internal groupoids, Mal'cev and protomodular categories, split exact sequence, algebraic exponentiation

2010 MSC: 18G50, 18D35, 20J15, 08C05

Theory and Applications of Categories, Vol. 28, 2013, No. 5, pp 150-65.

Published 2013-03-11.


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