9 citations · 13 across the 9 of their papers we have counts for
9 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…
Machine Space I: Weak exponentials and quantification over compact spaces
Peter F. Faul, Graham Manuell
Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties th…
Artin glueings of toposes as adjoint split extensions
Peter F. Faul, Graham Manuell, José Siqueira
Artin glueings of frames correspond to adjoint split extensions in the category of frames and finite-meet-preserving maps. We extend these ideas to the setting of toposes and show…
2-dimensional bifunctor theorems and distributive laws
Peter F. Faul, Graham Manuell, Jose Siqueira
In this paper we consider the conditions that need to be satisfied by two families of pseudofunctors with a common codomain for them to be collated into a bifunctor. We observe sim…
Quotients of monoid extensions and their interplay with Baer sums
Peter Faul, Graham Manuell
Cosetal extensions of monoids generalise extensions of groups, special Schreier extensions of monoids and Leech's normal extensions of groups by monoids. They share a number of pro…
Artin glueings of frames as semidirect products
Peter F. Faul, Graham R. Manuell
Artin glueings provide a way to reconstruct a frame from a closed sublocale and its open complement. We show that Artin glueings can be described as the weakly Schreier split exten…