From the 1 of 5 linked papers with an AI index.
5 papers
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…
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…
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…