Monodromy groupoid of an internal groupoid in topological groups with operations

Abstract

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.

Group-groupoid actions and liftings of crossed modules

“…Moreover, she developed cohomology theory of internal categories, equivalently, crossed modules, in categories of groups with operations [8] and [9]. The equivalences of the categories in [7,Theorem 1] and [19,Section 3] enable us to generalize some results on groupgroupoids to the more general internal groupoids for a certain algebraic category C (see for example [1], [14], [15] and [17]).…”

Categories internal to crossed modules

“…Mucuk et al [18] interpret the concept of normal subcrossed module and quotient crossed module concepts in the category of internal categories within groups, that is group-groupoids. The equivalences of the categories given in [8,Theorem 1] and [24,Section 3] enable us to generalize some results on groupgroupoids to the more general internal groupoids for an arbitrary category of groups with operations (see for example [1], [15], [16] and [17]).…”

Normality and quotient in the category of crossed modules within the category of groups with operations

“…Moreover, she developed cohomology theory of internal categories, equivalently, crossed modules, in categories of groups with operations [9] and [10]. The equivalences of the categories in [7] and [26] enable us to generalize some results on group-groupoids which are internal categories within groups to the more general internal groupoids for a certain algebraic category C (see for example [1], [21], [23] and [19]).…”