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Locally Commutative Categories

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Automata, Languages and Programming (ICALP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

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Abstract

It is known that a finite category can have all its base monoids in a variety V (i.e. be locally V, denoted ℓ V) without itself dividing a monoid in V (i.e. be globally V, denoted gV). This is in particular the case when V=Com, the variety of commutative monoids. Our main result provides a combinatorial characterization of locally commutative categories. This is the first such theorem dealing with a variety for which local differs from global. As a consequence, we show that ℓ Com ⊂ gV for every variety V that strictly contains the commutative monoids.

Research supported in part by NSERC and FCAR grants.

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Author information

Authors and Affiliations

  1. School of Computer Science, McGill University, 3480 rue University, Montréal, PQ, H3A 2A7, Canada

    Arkadev Chattopadhyay & Denis Thérien

Authors
  1. Arkadev Chattopadhyay
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  2. Denis Thérien
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

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© 2003 Springer-Verlag Berlin Heidelberg

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Chattopadhyay, A., Thérien, D. (2003). Locally Commutative Categories. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_76

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  • DOI: https://doi.org/10.1007/3-540-45061-0_76

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

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