In this paper, we show that every selective groupoid induced by a fuzzy subset is a pogroupoid, and we discuss several properties in quasi ordered sets by introducing the notion of a framework.

In this paper, we show that every selective groupoid induced by a fuzzy subset is a pogroupoid, and we discuss several properties in quasi ordered sets by introducing the notion of a framework.

We study the mathematical structure of notion measurement space, which extends aspects noncommutative topology that are based on quantale theory. This yields a geometric model physical measurements provides realist picture, yet also operational, such and classical information arise interdependently as primitive concepts. A derived observer caters for formulation Bohr's classical/quantum divide....

A groupoid is a small category in which each morphism has an inverse. A topological groupoid is a groupoid in which both sets of objects and morphisms have topologies such that all maps of groupoid structure are continuous. The notion of monodromy groupoid of a topological groupoid generalizes those of fundamental groupoid and universal cover. It was earlier proved that the monodromy groupoid o...

In this work we deal with actions of vector groupoid which is a new concept in the literature‎. ‎After we give the definition of the action of a vector groupoid on a vector space‎, ‎we obtain some results related to actions of vector groupoids‎. ‎We also apply some characterizations of the category and groupoid theory to vector groupoids‎. ‎As the second part of the work‎, ‎we define the notion...

We propose a notion of groupoid homotopy for generalized maps. This notion of groupoid homotopy generalizes the notions of natural transformation and strict homotopy for functors. The groupoid homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As an application we consider orbifolds as groupoids and study the orbifold homotopy between orbifold maps induced by the...

The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.

In this paper, we introduce the notion of a logistic groupoid on the real numbers R, and show that, given a groupoid (R, ?) with some conditions, there exists a groupoid (X, ~) such that (R, ?) is the logistic groupoid of (X, ~).

Motivated by the computations done in [9], where I introduced and discussed what I called the groupoid of generalized gauge transformations, viewed as a groupoid over the objects of the category BunG,M of principal G-bundles over a given manifold M , I develop in this paper the same ideas for the more general case of principal G-bundles or principal bundles with structure groupoid G, where now ...