相关论文: Group-groupoid actions and liftings of crossed mod…

In this paper we define the notion of pullback lifting of a lifting crossed module over a crossed module morphism and interpret this notion in the category of group-groupoid actions as pullback action. Moreover, we give a criterion for the…

In the theory of crossed modules, considering arbitrary self-actions instead of conjugation allows for the extension of the concept of crossed modules and thus the notion of generalized crossed module emerges. In this paper we give a…

In this paper we prove some results on the covering morphisms of internal groupoids. We also give a result on the coverings of the crossed modules of groups with operations.

In this paper using split extensions of group-groupoids we obtain the notion of crossed modules over group-grouoids which are also called 2-groups and we prove a categorical equivalence of these types of crossed modules and double…

It is a well known result in the covering groups that a subgroup $G$ of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic…

In this work we deal with coverings and actions of Lie group- groupoids being a sort of the structured Lie groupoids. Firstly, we define an action of a Lie group-groupoid on some Lie group and the smooth coverings of Lie group-groupoids.…

In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category $\mathsf{C}$ of groups with operations using the categorical equivalence between crossed modules and internal categories in…

The aim of this paper is to characterize the notion of internal category (groupoid) in the category of Leibniz algebras and investigate the properties of well-known notions such as covering groupoid and groupoid operations (actions) in this…

We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is…

In this paper we define the notions of normal subcrossed module and quotient crossed module within groups with operations; and using the equivalence of crossed modules over groups with operations and internal groupoids we prove how…

We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-like objects in the category of racks, generalizing the…

For any cssc-crossed module a category is constructed, equipped with a structure and proved that this is a coherent categorical group. Together with a result of the previous paper, where to any categorical group the cssc-crossed module is…

In this paper, we define the pullback crossed modules in the category of racks which mainly based on a pullback diagram of rack morphisms with extra crossed module data on some of its arrows. Furthermore we prove that the conjugation…

In this paper we will define notion homotopy of morphisms of crossed modules of Lie algebras. Then we construct a groupoid structure of Lie crossed module morphisms and their homotopies.

In this paper, we define the notion of crossed modules of groups with action and investigate related structures. Functions for computing of these structures have been written using the GAP computational discrete algebra programming…

We introduce the notion of Whitehead sequence which is defined for a base category together with a system of abstract actions over it. In the classical case of groups and group actions the Whitehead sequences are precisely the…

Topological groupoids admit various types of morphisms. We push these notions to the level of continuous groupoid actions to obtain various types of groupoid action morphisms. Some dynamical properties and their relation to these morphisms…

We provide concrete models for generalized morphisms and Morita equivalences of topological 2-groupoids by introducing the notions of crossings and crossed extensions of groupoid crossed modules. A systematic study of these objects is…

In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…

In this paper, we state the notion of morphisms in the category of abelian crossed modules and prove that this category is equivalent to the category of strict Picard categories and regular symmetric monoidal functors. The theory of…