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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…
Fibrational approach to Grandis exactness for 2-categories
Elena Caviglia, Zurab Janelidze, Luca Mesiti
In an abelian category, the (bi)fibration of subobjects is isomorphic to the (bi)fibration of quotients. This property captures substantial information about the exactness structur…
On extensions of Cohen Structure Theorem
Elena Caviglia, Amartya Goswami, Luca Mesiti
The aim of this paper is to extend Cohen structure theorem beyond local rings. Both Cohen structure theorem and Nagata's generalization of it are special cases of our results. We i…