3 papers
math.CT2025
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…
math.CT2025
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…
math.CT2025
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…