arXiv:2408.00562v1 [math.GR] 1 Aug 2024 Page 1 arXiv:2408.00562v1 [math.GR] 1 Aug 2024
1 The synthetic presentation of the main research directions in groupoid theory Gheorghe …

Using an algebraic point of view we present an introduction to the groupoid theory; that is,
we give fundamental properties of groupoids as uniqueness of inverses and properties of …

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Let G be a finite groupoid and α=(S_g,\alpha_g)_g∈G a unital partial action of group-type of
G on a commutative ring S=y∈G_0S_y. We prove a Galois correspondence between a …

In this paper, we introduce the concept of partial groupoid actions on R-semicategories as
well as we give criteria for existence of a globalization of it. This point of view is a …

Some conditions for the Galois map to be injective are given in the groupoid acting on a
noncommutative ring context. In the particular case in which the Galois extension is a central …

We provide a correspondence between one-sided coideal subrings and one-sided ideal two-
sided coideals in an arbitrary bialgebroid. We prove that, under some expected additional …

We introduce maximal ordered groupoids and study some of their properties. Also, we use
the Ehresmann–Schein–Nambooripad Theorem, which establishes a one-to-one …

We show a classification method for finite groupoids using a decomposition of its connected
components on a product of a coarse groupoid and of an isotropy group. Moreover, we …