9 citations · 18 across the 12 of their papers we have counts for
13 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…
F-Inverse Monoids as Weakly Schreier Extensions
Peter F. Faul
It is known that an inverse monoid is E-unitary if and only if the following diagram is an extension: , where is the semilattice of idempotents and $…
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…
The Reverse Representation Problem
Peter F. Faul, Zurab Janelideze, Gideo Joubert
Cayley's theorem tells us that all groups occur as subgroups of the group of automorphisms over some set . In this paper we consider a `sort-of' converse to this qu…
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…
A Survey of Schreier-Type Extensions of Monoids
P. F. Faul
We give an overview of a number of Schreier-type extensions of monoids and discuss the relation between them. We begin by discussing the characterisations of split extensions of gr…
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…
Baer sums for a natural class of monoid extensions
Peter Faul
It is well known that the set of isomorphism classes of extensions of groups with abelian kernel is characterized by the second cohomology group. In this paper we generalise this c…
-Semidirect Products of Inverse Monoids are Weakly Schreier Extensions
Peter Faul
A split extension of monoids with kernel k: N -> G, cokernel e: G -> H and splitting s: H -> G is weakly Schreier if each element g in G can be written g = k(n)se(g) for some n in…
A characterization of weakly Schreier extensions of monoids
P. F. Faul
A split extension of monoids with kernel , cokernel and splitting is Schreier if there exists a unique set-theoretic map $q…
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…