Related papers: Generalized groups and module groupoids
In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established.
The aim of this paper is to describe the definitions and main properties of three generalizations of the group concept, namely: groupoid, generalized group and almost groupoid. Some constructions of these algebraic structures and…
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…
This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.
The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.
The aim of this paper is to explain, mostly through examples, what groupoids are and how they describe symmetry. We will begin with elementary examples, with discrete symmetry, and end with examples in the differentiable setting which…
We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.
Some results that are true in classical groups are investigated in generalized groups and are shown to be either generally true in generalized groups or true in some special types of generalized groups. Also, it is shown that a Bol groupoid…
In this paper, we will introduce two generalizations of second submodules of a module over a commutative ring and explore some basic properties of these classes of modules.
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…
In this work, we will introduce the notion of generalized topological groups using generalized topological structure and generalized continuity defined by ?A. Cs?asz?ar [2]. We will discuss some basic properties of this kind of structures…
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…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
In this paper, we define a new structure analogous to group, called partial group. This structure concerns the partial stability by the composition inner law. We generalize the three isomorphism theorems for groups to partial groups.
We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopical construction of a double groupoid from a triad consisting…
A group, defined as set with associative multiplication and inverse, is a natural structure describing the symmetry of a space. The concept of group generalizes to group objects internal to other categories than sets. But there are yet more…
In this paper, we mainly discuss some generalized metric properties and the character of the free paratopological groups, and extend several results valid for free topological groups to free paratopological groups.
In this short note, we argue that directed homotopy can be given the structure of generalized modules, over particular monoids. This is part of a general attempt for refoundation of directed topology.
The article $-$ part of a larger thesis which aims to give a detailed description of the generalisation to the category of groups with operators of the classical theory of semisimplicity for modules $-$ presents a straightforward…
Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…