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Cancellative Convex Semilattices
Ana Sokolova, Harald Woracek
https://arxiv.org/abs/2507.11186 https://arxiv.org/pdf/2507.11186

Cancellative Convex Semilattices
Convex semilattices are algebras that are at the same time a convex algebra and a semilattice, together with a distributivity axiom. These algebras have attracted some attention in the last years as suitable algebras for probability and nondeterminism, in particular by being the Eilenberg-Moore algebras of the nonempty finitely-generated convex subsets of the distributions monad. A convex semilattice is cancellative if the underlying convex algebra is cancellative. Cancellative convex algebra…

Presentations for semigroups of full-domain partitions
Luka Carroll, James East, Matthias Fresacher
https://arxiv.org/abs/2507.05497 https://

Presentations for semigroups of full-domain partitions
The full-domain partition monoid $P_n^{fd}$ has been discovered independently in two recent studies on connections between diagram monoids and category theory. It is a right restriction Ehresmann monoid, and contains both the full transformation monoid and the join semilattice of equivalence relations. In this paper we give presentations (by generators and relations) for $P_n^{fd}$, its singular ideal, and its planar submonoid. The latter is not an Ehresmann submonoid, but it is a so-called grr…

This https://arxiv.org/abs/2403.05295 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Inverse semigroups of separated graphs and associated algebras
In this paper we introduce an inverse semigroup $\mathcal{S}(E,C)$ associated to a separated graph $(E,C)$ and describe its internal structure. In particular we show that it is strongly $E^*$-unitary and can be realized as a partial semidirect product of the form $\mathcal{Y}\rtimes\mathbb{F}$ for a certain partial action of the free group $\mathbb{F}=\mathbb{F}(E^1)$ on the edges of $E$ on a semilattice $\mathcal{Y}$ realizing the idempotents of $\mathcal{S}(E,C)$. In addition we also describe…