  "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.
