The aim of this paper is to obtain a group-2-groupoid as 2-groupoid object in the category groups and also special kind an internal group-groupoids. Corresponding group-2-groupoids, we some categorical structures related crossed modules group-groupoids prove equivalences between them. These results enable us 2-dimensional notions

Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.

Roughly speaking, two dynamical systems are transversally equivalent if they have the same space of orbits; a property is transverse if it is preserved under transverse equivalence. Various notions of transverse equivalence have been defined: among them, similarity of measured groupoids, Morita equivalence of locally compact groupoids, stable orbit equivalence of measure equivalence relations. ...

In this work, we study the integrability of quotients quasi-Poisson manifolds. Our approach allows us to put several classical results about Poisson in a common framework. By categorifying one already known methods reducing symplectic groupoids also describe double groupoids, which integrate recently introduced groupoid structures on gauge groupoids.

We propose a definition of compact quantum groupoids in the setting of C -algebras, associate to such a quantum groupoid a regular C -pseudo-multiplicative unitary, and use this unitary to construct a dual Hopf C -bimodule and to pass to a measurable quantum groupoid in the sense of Enock and Lesieur. Moreover, we discuss examples related to compact and to étale groupoids and study principal co...

the aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered ag-groupoids with left identity. these concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered ag-groupoids, so it seems to be interesting to study them.

The aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered AG-groupoids with left identity. These concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered AG-groupoids, so it seems to be interesting to study them.

Abstract Here $${\underline{M}}$$ M ̲ denotes a pair ( M , A ) of manifold and subset (e.g. $$A=\partial M$$ A = ∂ or $$A=\varnothing $$ ∅ ). We construct for each its motion g...

An arbitrary Lie groupoid gives rise to a groupoid of germs of local diffeomorphisms over its base manifold, known as its e ect. The e ect of any bundle of Lie groups is trivial. All quotients of a given Lie groupoid determine the same e ect. It is natural to regard the e ects of any two Morita equivalent Lie groupoids as being equivalent . In this paper we shall describe a systematic way of co...

Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B of A which is embedded with a strong structure S. In [9], Kandasamy studied the concept of Smarandache groupoids, subgroupoids, ideal of groupoids, seminormal subgroupoids, Smarandache Bol groupoids, and strong Bol groupoids and obtained many interesting resul...