8 papers
On the zero-classes of monoid semi-congruences
M. Hoefnagel, N. Martins-Ferreira, M. Sobral
This paper studies the zero-classes of monoid semi-congruences, understood as internal reflexive relations on a monoid. Classical examples include normal submonoids, which arise as…
Strict monadic topology II: descent for closure spaces
George Janelidze, Manuela Sobral
By a closure space we will mean a pair , in which is a set and a set of subsets of closed under arbitrary intersections. The purpose of this…
A note on idempotent semirings
George Janelidze, Manuela Sobral
For a commutative semiring S, by an S-algebra we mean a commutative semiring A equipped with a homomorphism from S to A. We show that the subvariety of S-algebras determined by the…
On the normality of monoid monomorphisms
Nelson Martins-Ferreira, Manuela Sobral
In the category of monoids we characterize monomorphisms that are normal, in an appropriate sense, to internal reflexive relations, preorders or equivalence relations. The zero-cla…
Schreier split extensions of preordered monoids
Nelson Martins-Ferreira, Manuela Sobral
Properties of preordered monoids are investigated and important subclasses of such structures are studied. The corresponding full subcategories of the category of preordered monoid…
Split extensions and semidirect products of unitary magmas
Marino Gran, George Janelidze, Manuela Sobral
We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivale…
Cancellative conjugation semigroups and monoids
A. P. Garrão, N. Martins-Ferreira, M. Raposo +1
We show that the category of cancellative conjugation semigroups is weakly Mal'tsev and give a characterization of all admissible diagrams there. In the category of cancellative co…
On some categorical-algebraic conditions in S-protomodular categories
Nelson Martins-Ferreira, Andrea Montoli, Manuela Sobral
In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cart…