# Lambek pregroups are Frobenius spiders in preorders

arXiv: https://arxiv.org/abs/2105.03038 · HTML: https://mlsanity.com/paper/2105.03038/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 73 references that are in the map.
- First posted on arXiv 7 May 2021.

## Builds on (most cited first, 13 of 13)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer](https://mlsanity.com/paper/2102.12846/) (2021)
- [Quantum Natural Language Processing on Near-Term Quantum Computers](https://mlsanity.com/paper/2005.04147/) (2020)
- [The Frobenius anatomy of word meanings I: subject and object relative pronouns](https://mlsanity.com/paper/1404.5278/) (2014)
- [Lambek vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus](https://mlsanity.com/paper/1302.0393/) (2013)
- [The Frobenius anatomy of word meanings II: possessive relative pronouns](https://mlsanity.com/paper/1406.4690/) (2014)
- [Translating and Evolving: Towards a Model of Language Change in DisCoCat](https://mlsanity.com/paper/1811.11041/) (2018)
- [Compositionality for Recursive Neural Networks](https://mlsanity.com/paper/1901.10723/) (2019)
- [A Frobenius Algebraic Analysis for Parasitic Gaps](https://mlsanity.com/paper/2005.05639/) (2020)
- [Monoidal computer III: A coalgebraic view of computability and complexity](https://mlsanity.com/paper/1704.04882/) (2017)
- [Bicompletions of distance matrices](https://mlsanity.com/paper/1303.6428/) (2013)
- [Towards concept analysis in categories: limit inferior as algebra, limit superior as coalgebra](https://mlsanity.com/paper/1505.01098/) (2015)
- [Functorial Semantics for Partial Theories](https://mlsanity.com/paper/2011.06644/) (2020)

## Built on by (most cited first, 1 of 1)

- [Grammar Equations](https://mlsanity.com/paper/2106.07485/) (2021)

## Abstract (arXiv)

"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.