Related papers: Partial Groupoid Actions on Categories: Globalizat…
In this paper we introduce the notion of a partial action of a groupoid on a ring as well as we give a criteria for the existence of a globalization of it. We construct a Morita context associated to a globalizable partial groupoid action…
In this work, we introduce the notion of a partial action of a group on a strict monoidal category. We propose, in the context of Monoidal categories, new constructions analogous to those existing for partial group actions over an algebra…
The main goal of this paper is to introduce the notion of twisted partial action of groupoids. We generalize the theorem about the existence of an enveloping action, also known as the globalization theorem, and show that the crossed…
We introduce (continuous) partial category actions on sets (topological spaces) and show that each such action admits a universal globalization. Thereby, we obtain a simultaneous generalization of corresponding results for groups, by…
We introduce partial semigroupoid actions on sets and demonstrate that each such action admits universal globalization. Our construction extends the universal globalization for partial category actions given by P. Nystedt (Lundstr\"om) and…
In this paper we introduce the definition of partial action on small $k$-categories generalizing the similar well known notion of partial actions on algebras. The point of view of partial action which we use in this paper is the one which…
In this paper we introduce the notion of partial action of a weak Hopf algebra on algebras, unifying the notions of partial group action [11], partial Hopf action ([2],[3],[9]) and partial groupoid action [4]. We construct the fundamental…
We propose two universal constructions of globalization of a partial action of a semigroup on a set, satisfying certain conditions which arise in Morita theory of semigroups. One of the constructions is based on the tensor product of a…
In this paper, we are interested in the study of the existence of connections between partial groupoid actions and partial group actions. Precisely, we prove that there exists a datum connecting a partial action of a connected groupoid and…
We provide a necessary and sufficient condition to the existence of an ordered globalization of a partial ordered action of an ordered groupoid on a ring and we also present criteria to obtain uniqueness. Furthermore, we apply those results…
We present some constructions of groupoids as: direct product, semidirect product, and we give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient…
Let $M$ be a monoid, $\mathscr{C}$ a category with pullbacks and $X$ an object of $\mathscr{C}$. We introduce the notion of a partial action $\alpha$ of $M$ on $X$ and study the globalization question for $\alpha$. If $\alpha$ admits a…
In this paper we introduce the notions of partial bimodule algebra and partial bico- module algebra. We also deal with the existence of globalizations for these structures, generalizing related results appeared in [2, 4]. As an application…
In this paper we consider categories over a commutative ring provided either with a free action or with a grading of a not necessarily finite group. We define the smash product category and the skew category and we show that these…
Let $\operatorname{G}$ be a finite groupoid and $\alpha=(S_g,\alpha_g)_{g\in \operatorname{G}}$ a unital partial action of group-type of $\operatorname{G}$ on a commutative ring $S=\oplus_{y\in\operatorname{G}_0}S_y$. We shall prove a…
We prove that every partial action of an inverse semigroupoid on a set admits a universal globalization. Moreover, we show that our construction gives a reflector from the category of partial actions on the full subcategory of global…
We prove that every ordered partial action of an inverse semigroupoid on a partially ordered set admits a globalization. This result is used to establish a connection between ordered partial actions of groupoids and a multi-object analogue…
The effectiveness of the aplication of constructions in $G$-graded $k$-categories to the computation of the fundamental group of a finite dimensional $k$-algebra, alongside with open problems still left untouched by those methods and new…
Given a partial (resp. a global) action $\alpha$ of a connected finite groupoid $G$ on a ring $A$, we determine necessary and sufficient conditions for the partial (resp. global) skew groupoid ring $A\star_{\alpha} G$ to be a separable…
We consider the category of partial actions, where the group and the set upon which the group acts can vary. Within this framework, we develop a theory of quotient partial actions and prove that this category is both (co)complete and…