6 papers
A comparison between weakly protomodular and protomodular objects in unital categories
Xabier GarcÃa-MartÃnez, Andrea Montoli, Diana Rodelo +1
We compare the concepts of protomodular and weakly protomodular objects within the context of unital categories. Our analysis demonstrates that these two notions are generally dist…
Categorical-algebraic aspects of Heyting semilattices
Xabier GarcÃa-MartÃnez, James R. A. Gray, Michael A. Hoefnagel +2
This article gives an overview of some key categorical-algebraic properties of the variety of Heyting semilattices, with the aim of correcting a misconception in the literature. We…
Action accessible and weakly action representable varieties of algebras
Xabier GarcÃa-MartÃnez, Manuel Mancini
The main goal of this article is to investigate the relationship between action accessibility and weak action representability in the context of varieties of non-associative algebr…
On the coordinate rings of Calogero-Moser spaces and the invariant commuting variety of a pair of matrices
Farkhod Eshmatov, Xabier GarcÃa-MartÃnez, Zafar Normatov +1
This paper presents a comprehensive description of the coordinate rings and Poisson brackets associated with the fourth Calogero-Moser space and invariant commuting pairs of matric…
Weak representability of actions of non-associative algebras
Jose Brox, Xabier GarcÃa-MartÃnez, Xabier García-Martínez +3
We study the categorical-algebraic condition that internal actions are weakly representable (WRA) in the context of varieties of (non-associative) algebras over a field. Our first…
A universal Kaluzhnin--Krasner embedding theorem
Bo Shan Deval, Xabier GarcÃa-MartÃnez, Tim Van der Linden
Given two groups and , the Kaluzhnin--Krasner universal embedding theorem states that the wreath product acts as a universal receptacle for extensions from to $…