From the 1 of 11 linked papers with an AI index.
11 papers
A Mayer-Vietoris calculus for regular denominators
Elena Caviglia, Amartya Goswami
Let be a commutative ring and let be an ideal. An element is a regular denominator for when multiplication by on is injective; we denote the set of a…
Clifford semigroups and the monoidal Grothendieck construction
Elena Caviglia, Peter F. Faul, Graham Manuell +1
The paper shows that the known correspondence between Clifford semigroups and functors from a semilattice to groups arises from the monoidal Grothendieck construction, uses this to…
Generalized action monads and descent
Elena Caviglia, Sophie Marques, Luca Mesiti
We develop a monadic approach to actions of internal categories. Given an internal category, we construct a monad on a slice whose algebras are the actions of that internal categor…
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…