8 papers
From subtractive ideals of semirings to deductive and inductive sets in general algebras
Elena Caviglia, Amartya Goswami, Zurab Janelidze +2
In this paper we extend the characterisation of kernels in semirings as subtractive ideals to general algebras. We then analyse the counterparts of ``subtractive'' and ``ideal'' in…
Comonadic approach to pretorsion theories
Elena Caviglia, Zurab Janelidze, Luca Mesiti
We present a comonadic approach to pretorsion theories on semiexact categories, i.e. categories equipped with a closed ideal of null morphisms that admits all kernels and all coker…
Unicoherence in Locales
Elena Caviglia, Luca Mesiti, Cerene Rathilal
In this paper, we generalize the concept of unicoherence to the context of frames. Unicoherence, originally introduced by Kuratowski, is a connectedness property that is well studi…
Double Orthogonal Factorization Systems
C. B. Aberlé, Elena Caviglia, Matthew Kukla +4
We define strict and lax orthogonal factorization systems on double categories. These consist of an orthogonal factorization system on arrows and one on double cells that are compa…
Primitive quantales
Amartya Goswami, Elena Caviglia, Luca Mesiti
We generalize Jacobson's notion of primitive ring to the setting of quantales. We show that every primitive ring gives rise to a primitive quantale of ideals. We then prove a densi…
Rectangular torsion theories
Elena Caviglia, Zurab Janelidze, Luca Mesiti
In this paper we introduce and study \emph{rectangular torsion theories}, i.e.\ those torsion theories $(\C,\T,\F)$ with $\C$ a pointed category, where the canonical functor $\C\to…