4 papers
Clifford semigroups and the monoidal Grothendieck construction
Elena Caviglia, Peter F. Faul, Graham Manuell +1
We show that the monoidal Grothendieck construction can be applied to recover the known structure theorem for Clifford monoids, which states that they correspond to functors from a…
Bicategories of Lax Fractions
Graham Manuell, Lurdes Sousa
The well-known calculus of fractions of Gabriel and Zisman provides a convenient way to formally invert morphisms in a category. This was generalised to bicategories by Pronk. We e…
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…
The Case for Inverse Semirings
Peter F. Faul, Amartya Goswami, Gideo Joubert +1
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a…