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Thaísa Tamusiunas

Publications and source records attributed to Thaísa Tamusiunas.

At least 19 recordsLinked to original sources
arXiv2026

An Ehresmann-Schein-Nambooripad-type theorem for left restriction semigroupoids

We introduce the concept of locally inductive constellations and establish isomorphisms between the categories of left restriction semigroupoids and locally inductive constellations. This construction offers an alternative to the celebrated Ehresmann-Schein-Nambooripad (ESN) Theorem and, in particular, generalizes results for one-sided restriction semigroups. We also obtain ESN-type theorems for one-sided restriction categories and inverse semigroupoids.

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arXiv2026

A Generalization of the Ehresmann-Schein-Nambooripad Theorem to Two-Sided Ehresmann Semigroupoids

We introduce the notion of two-sided Ehresmann semigroupoids and show that they are in correspondence with a specific class of categories, which we call local biordered Ehresmann categories. This correspondence provides a unified generalization of the Ehresmann-Schein-Nambooripad Theorem for both inverse semigroupoids and Ehresmann semigroups. In particular, two-sided restriction semigroupoids form a distinguished subclass of two-sided Ehresmann semigroupoids, and for this case we describe the associated class of categories, extending earlier results for restriction semigroups.

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arXiv2026

Reflectors and the Globalization Problem for Partial Actions of Semiconstellations

We introduce semiconstellations and restriction semiconstellations, together with their actions on sets, providing a common setting for partial actions of categories, inverse semigroupoids, restriction semigroups, and semigroupoids. We then investigate the \emph{globalization problem}, which asks whether every partial action can, up to isomorphism, be obtained by restricting a global action. A distinctive feature of our approach is the use of reflectors not only to construct globalizations, but also to study when partial actions are globalizable. We show that every partial action of a restriction semiconstellation admits a reflector in the full subcategory of $S$-algebras consisting of what we call \emph{almost global actions}, and investigate conditions under which this reflector provides a globalization. As an application, we obtain a positive answer to the globalization problem for partial actions of restriction semigroupoids on sets, and consequently for restriction semigroups and restriction categories. In contrast, the answer is negative for restriction semiconstellations in general. Finally, given a semiconstellation $S$ and a suitable equivalence relation $R$ on $S$, we introduce the notion of an \emph{$R$-compatible action of} $S$ and construct a restriction semiconstellation $S^R$. We then show that partial and $R$-compatible actions of $S$ correspond, respectively, to partial and global actions of $S^R$. In this way, the globalization problem for semiconstellations can be reduced to the corresponding problem for restriction semiconstellations.

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arXiv2026

Groupoid Twisted Partial Actions

We introduce twisted partial actions of groupoids and establish necessary and sufficient conditions for the existence of a globalization. We prove that the crossed products associated with a twisted partial action and with its globalization are Morita equivalent. Finally, we extend partial projective representations and partial Schur multipliers to the groupoid setting and describe their interaction with twisted partial actions of groupoids.

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arXiv2026

The Szendrei Expansion of Restriction Semigroupoids

We introduce the concept of a restriction semigroupoid S, which unifies the notion of restriction semigroups and restriction categories within a single structure. We prove a representation theorem, showing that every restriction semigroupoid can be embedded into a determined category of partial maps. Furthermore, we construct the Szendrei expansion Sz(S) of S and establish that each premorphism between two restriction semigroupoids S and T is uniquely factorized by a morphism between the Szendrei expansion Sz(S) and T.

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arXiv2025

Partial Semigroupoid Actions on Sets

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 (Lundström) and the tensor product globalization for strong partial semigroup actions given by G. Kudryavtseva and V. Laan, thereby unifying the theory of partial actions for both categories and semigroups.

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arXiv2025

Galois Correspondence for Partial Groupoid Actions

We prove a Galois correspondence theorem for groupoids acting orthogonally and partially on commutative rings. We also consider partial actions that are not orthogonal, presenting two correspondences in this case: one for strongly Galois partial groupoid actions and one for global groupoid actions (without restriction). Some examples are presented.

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arXiv2025

Globalization of Partial Actions of Ordered Groupoids on Rings

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 to obtain a Morita context and to show that an inverse semigroup partial action has a globalization (unique up to isomorphism) if, and only if, it is unital.

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arXiv2025

Galois Theory under inverse semigroup actions

We develop a Galois theory of commutative rings under actions of finite inverse semigroups. We present equivalences for the definition of Galois extension as well as a Galois correspondence theorem. We also show how the theory behaves in the case of inverse semigroups with zero.

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arXiv2024

Weak Partial Representations

We introduce the notion of partial representation of a weak Hopf algebra. We present the universal algebra $H_{par}^w$, which factorizes these partial representations by algebra morphisms. Also, it is shown that $\Hp$ is isomorphic to a partial smash product, that it has the structure of a Hopf algebroid and also that it can be endowed with a quantum inverse semigroup structure. Moreover, it is shown that the algebra objects in the module category over $H_{par}^w$ correspond to symmetrical partial module algebras.

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arXiv2023

Inverse Semigroupoid Actions and Representations

We show that there is a one-to-one correspondence between the partial actions of a groupoid $G$ on a set $X$ and the inverse semigroupoid actions of the Exel's inverse semigroupoid $S(G)$ on $X$. We also define inverse semigroupoid representations on a Hilbert space $H$, as well as the Exel's partial groupoid $C^*$-algebra $C_p^*(G)$, and we prove that there is a one-to-one correspondence between partial groupoid representations of $G$ on $H$, inverse semigroupoid representations of $S(G)$ on $H$ and $C^*$-algebra representations of $C_p^*(G)$ on $H$.

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arXiv2023

Injectivity of the Galois map

Given a Galois extension $R^β \subset R$, where $β$ is an action of a finite groupoid on a noncommutative ring, we present some conditions to the Galois map be injective.

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arXiv2021

Partial Hopf-Galois theory

We develop a partial Hopf-Galois theory for partial H-module algebras and we recover analogs of classical results for Hopf algebras.

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arXiv2021

Groupoid Actions on Sets, Duality and a Morita Context

Let G and K be groupoids. We present the notion of a (G_α,K_β)-set and we prove a duality theorem in this context, which extends the duality theorem for graded algebras by groups. For A a unital G-graded algebra and X a finite split G-set, we show that there is an isomorphism between the category of the left A-modules X-graded and the category of the left A \#_α^{G}X-modules. As an application of this isomorphism, we construct a Morita context.

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arXiv2021

Galois correspondence for group-type partial actions of groupoids

Let $\operatorname{G}$ be a finite groupoid and $α=(S_g,α_g)_{g\in \operatorname{G}}$ 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 Galois correspondence between a class of wide subgroupoids of $\operatorname{G}$ and a class of subrings of $S$. We recover known results for global groupoid actions and we give several examples to illustrate the correspondence.

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arXiv2021

Galois Theory for Inverse Semigroup Orthogonal Actions

A Galois correspondence theorem is proved for the case of inverse semigroups acting orthogonally on commutative rings as a consequence of the Galois correspondence theorem for groupoid actions. To this end, we use a classic result of inverse semigroup theory that establishes a one-to-one correspondence between inverse semigroups and inductive groupoids.

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