7 papers
An Ehresmann-Schein-Nambooripad-type theorem for left restriction semigroupoids
Rafael Haag, Wesley G. Lautenschlaeger, Thaísa Tamusiunas
We introduce the concept of locally inductive constellations and establish isomorphisms between the categories of left restriction semigroupoids and locally inductive constellation…
The Szendrei Expansion of Restriction Semigroupoids
Rafael Haag, Wesley G. Lautenschlaeger, Thaísa 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…
Galois Theory under inverse semigroup actions
Wesley G. Lautenschlaeger, Thaísa 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…
Galois Correspondence for Partial Groupoid Actions
Wesley G. Lautenschlaeger, Thaísa 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…
Globalization of Partial Actions of Ordered Groupoids on Rings
Wesley G. Lautenschlaeger, Thaísa 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…
Partial groupoid representations and a relation with the Birget-Rhodes expansion
Wesley G. Lautenschlaeger, Thaísa Tamusiunas
We introduce partial representation of a finite groupoid on an algebra and show that the partial groupoid representations of are in one-to-one correspondence with the r…