13 papers
Partial Linearity in Categories
Roy Ferguson, Zurab Janelidze
In this paper we generalise the notion of linearity (in the sense of Lawvere) to a category C equipped with a compatible sum structure and product structure. In this context, any m…
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…
Homological lemmas for (non-abelian) group-like structures by diagram chasing in a self-dual context
Kishan Kumar Dayaram, Amartya Goswami, Zurab Janelidze +2
Through abelian categories, homological lemmas for modules admit a self-dual treatment, where half of the proof of a lemma is sufficient to prove the full lemma. In this paper, we…
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…
Frobenius reciprocity, modular connections, lattice isomorphism theorem and abstract principal ideals
Amartya Goswami, Zurab Janelidze, Graham Manuell
The purpose of this short note is to fill a gap in the literature: Frobenius reciprocity in the theory of doctrines is closely related to modular connections in projective homologi…