6 papers
The Szendrei Expansion of Restriction Semigroupoids
Rafael Haag, Wesley G. Lautenschlaeger, ThaÃsa Tamusiunas
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 repres…
Groupoid Twisted Partial Actions
Laerte Bemm, Wesley G. Lautenschlaeger, ThaÃsa Tamusiunas
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 associa…
An Ehresmann-Schein-Nambooripad-type theorem for left restriction semigroupoids
Rafael Haag, Wesley G. Lautenschlaeger, ThaÃsa Tamusiunas
We introduce the concept of locally inductive constellations and establish isomorphisms between the categories of left restriction semigroupoids and locally inductive constellation…
Galois Correspondence for Partial Groupoid Actions
Wesley G. Lautenschlaeger, ThaÃsa Tamusiunas
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…
Galois Theory under inverse semigroup actions
Wesley G. Lautenschlaeger, ThaÃsa Tamusiunas
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 corre…
Globalization of Partial Actions of Ordered Groupoids on Rings
Wesley G. Lautenschlaeger, ThaÃsa Tamusiunas
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 criter…