# Free compact 2-categories

@article{Preller2007FreeC2, title={Free compact 2-categories}, author={Anne Preller and Joachim Lambek}, journal={Mathematical Structures in Computer Science}, year={2007}, volume={17}, pages={309 - 340} }

Before one can attach a meaning to a sentence, one must distinguish different ways of parsing it. When analysing a language with pregroup grammars, we are thus led to replace the free pregroup by a free compact strict monoidal category. Since a strict monoidal category is a 2-category with one 0-cell, we investigate the free compact 2-category generated by a given category, and describe its 2-cells as labelled transition systems. In particular, we obtain a decision procedure for the equality of…

## 53 Citations

Compact Monoidal Categories from Linguistics to Physics

- Mathematics
- 2010

This is largely an expository paper, revisiting some ideas about compact 2-categories, in which each 1-cell has both a left and a right adjoint. In the special case with only one 0-cell (where the…

Toward discourse representation via pregroup grammars

- LinguisticsJ. Log. Lang. Inf.
- 2007

Every pregroup grammar is shown to be strongly equivalent to one which uses basic types and left and right adjoints of basic types only. Therefore, a semantical interpretation is independent of the…

Toward Discourse Representation via Pregroup

- Philosophy
- 2007

Every pregroup grammar is shown to be strongly equivalent to one which uses basic types and left and right adjoints of basic types only. Therefore a semantical interpretation is independent of the…

Complexity of Grammar Induction for Quantum Types

- LinguisticsQPL
- 2014

It is shown that for a variety of type systems, including pivotal and compact closed categories, the grammar induction problem is NP-complete, and could be extended to linguistic type systems such as autonomous or bi-closed categories.

Pregroup Grammars and Context-free Grammars

- Computer Science
- 2007

This work presents a direct construction of a context-free grammar and a push-down automaton, equivalent to a given pregroup grammar, based on a full system of Compact Bilinear Logic.

Agreement and Cliticization in Italian: A Pregroup Analysis

- LinguisticsLATA
- 2010

This paper presents an analysis of features specification and agreement based on the parallel computations of a type calculus involving two pregroups grammars: the free pregroup of syntactic types…

Cyclic pregroups and natural language: a computational algebraic analysis

- Linguistics, Computer ScienceCILC
- 2011

This paper proposes an extension of the calculus of pregroups by introducing appropriate cyclic rules that will allow the grammar to formally analyze and compute word order and movement phenomena in different languages such as Persian, French, Italian, Dutch and Hungarian.

Clitic Movement in Pregroup Grammar: A Cross-Linguistic Approach

- LinguisticsTbiLLC
- 2009

This paper proposes an extension of the calculus of pregroups including two cyclic rules and uses them to formally analyze movement of clitic clusters in Persian, French, and Italian.

Autonomization of Monoidal Categories

- MathematicsACT
- 2019

It is shown that contrary to common belief in the DisCoCat community, a monoidal category is all that is needed to define a categorical compositional model of natural language, and the applications of this principle to various distributional models of meaning are illustrated.

Towards functorial language-games

- Computer ScienceCAPNS@QI
- 2018

This work compositionally build game-theoretic semantics of sentences by taking the semantic category to be the category whose morphisms are open games, which requires some modifications to the grammar category to compensate for the failure of open games to form a compact closed category.

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