6 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…
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…
Principal 2-bundles and quotient 2-stacks
Elena Caviglia
We generalize principal bundles and quotient stacks to the two-categorical context of bisites. We introduce a notion of principal 2-bundle that makes sense for a 2-category with fi…
Generalized principal bundles and quotient stacks
Elena Caviglia
We consider the internalization of the usual notion of principal bundle in a site that has all pullbacks and a terminal object. We use this notion to consider the explicit construc…