Liftings of crossed modules in the category of groups with operations

In this paper we define the notion of lifting of a crossed module via the morphism in groups with operations and give some properties of this type of liftings. Further we prove that the lifting crossed modules of a certain crossed module are categorically equivalent to the internal groupoid actions on groups with operations, where the internal groupoid corresponds to the crossed module.

Monodromy groupoid of an internal groupoid in topological groups with operations

In this paper, the monodromy groupoids of internal groupoids in the topological groups with operations are studied and a monodromy principle for internal groupoids in groups with operations is obtained.