Crossed module aspects of monodromy groupoids for internal groupoids

The notion of monodromy groupoid was introduced by J. Pradines in [3] to generalize the standard construction of a simply connected Lie group from a Lie algebra to a construction of a Lie groupoid from a Lie algebroid and has been developed by many others. The categorical equivalence between internal groupoids and crossed modules in groups with operations is known by [2] as a generalization of an equivalence of crossed modules within groups and group-groupoids [1]. In this work using the former equivalence and techniques of crossed modules we give a construction of the monodromy groupoid for topological internal groupoids within groups with operations including groups, rings, associative algebras, associative commutative algebras, Lie algebras, Leibniz algebras, alternative algebras and some others.