"Spider" is a nickname of *special Frobenius algebras*, a fundamental structure from mathematics, physics, and computer science. *Pregroups* are a fundamental structure from linguistics. Pregroups and spiders have been used together in natural language processing: one for syntax, the other for semantics. It turns out that pregroups themselves can be characterized as pointed spiders in the category of preordered relations, where they naturally arise from grammars. The other way around , general spider algebras can be characterized as pregroup unions . This extends the characterization of spider algebras over sets and relations as disjoint unions of abelian groups. The compositional framework that emerged with the results suggests new ways to understand and apply the basis structures in machine learning and data analysis.
"Spider" is a nickname of *special Frobenius algebras*, a fundamental structure from mathematics, physics, and computer science. *Pregroups* are a fundamental structure from linguistics. Pregroups and spiders have been used together in natural language processing: one for syntax, the other for semantics. It turns out that pregroups themselves can be characterized as pointed spiders in the category of preordered relations, where they naturally arise from grammars. The other way around preordered spider algebras in general can be characterized as unions of pregroups . This extends the characterization of relational spider algebras as disjoint unions of groups. The compositional framework that emerged with the results suggests new ways to understand and apply the basis structures in machine learning and data analysis.
R
, general spider algebras
preordered spider algebras in general
R
pregroup unions
unions of pregroups
R
spider algebras over sets and relations
relational spider algebras
D
abelian