5 papers · 1 filter
Coherent and ideal actions in ideally exact categories
Manuel Mancini, Giuseppe Metere, Federica Piazza
In the context of ideally exact categories, we introduce the notions of internal coherent action and internal ideal action that generalise different aspects of unital actions of ri…
On the representability of actions of unital algebras
Manuel Mancini, Federica Piazza, Corentin Vienne
Working in the setting of ideally exact categories, we investigate the representability of actions of unital non-associative algebras over a field. We show that, in general, such c…
Weak action representability of 2-nilpotent groups
Alessandro Dioguardi Burgio, Manuel Mancini, Tim Van der Linden
In this article, we investigate the representability of actions of the category of -nilpotent groups. We first provide an algebraic characterisati…
On actions and split extensions in varieties of hoops: the case of strong section
Manuel Mancini, Giuseppe Metere, Federica Piazza
The aim of this article is to investigate internal actions and split extensions in the variety of hoops. We provide a characterization of split extensions with strong section in te…
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…