Free compact 2-categories

Volume 17
Issue 02 - Apr 2007
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<div style="background: #FFFFFF; margin: 10px 10px 10px 10px; padding: 10px 10px 10px 20px; text-align: left; border-top: 1px dashed #a5bbd1; border-left: 10px solid #a5bbd1; font-family: Verdana, Geneva, sans-serif;"><br> <div style="font-size: 12px; padding: 0px 0px 10px 0px; font-weight:bold; color: #003366;">Free compact 2-categories</div><br><div style="font-size: 10px;"><b>ANNE PRELLER and JOACHIM LAMBEK (2007).</b><br /> <a href="http://journals.cambridge.org/action/displayJournal?jid=MSC">Mathematical Structures in Computer Science</a>, <a href="http://journals.cambridge.org/action/displayJournal?jid=MSC&volumeId=17&bVolume=y#loc17 ">Volume 17</a>, <a href="http://journals.cambridge.org/action/displayIssue?jid=MSC&volumeId=17&issueId=02&iid=1003848"> Issue 02</a>, April 2007 pp 309-340 <br/> <a href="http://journals.cambridge.org/action/displayAbstract?aid=1003848">http://journals.cambridge.org/action/displayAbstract?aid=1003848</a></div></div>
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Free compact 2-categories

ANNE PRELLER and JOACHIM LAMBEK (2007).
Mathematical Structures in Computer Science, Volume 17, Issue 02, April 2007 pp 309-340 http://journals.cambridge.org/action/displayAbstract?aid=1003848

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Mathematical Structures in Computer Science (2007), 17 : 309-340 Cambridge University Press

doi:10.1017/S0960129506005901 (About doi)

Published online by Cambridge University Press 18 Jan 2007

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Mathematical Structures in Computer Science (2007), 17:309-340 Cambridge University Press

doi:10.1017/S0960129506005901

Paper

Free compact 2-categories

ANNE PRELLER^a1 and JOACHIM LAMBEK^a2

^a1LIRMM/CNRS Montpellier, France Email: preller@lirmm.fr

^a2McGill University Montréal, QC, Canada Email: lambek@math.mcgill.ca

Article author query

preller a

lambek j

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 2-cells in the free compact 2-category.

(Received October 10 2005)

(Revised May 15 2006)

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