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Preframe presentations present

  • Part I
  • Conference paper
  • First Online:
Category Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1488))

Abstract

Preframes (directed complete posets with finite meets that distribute over the directed joins) are the algebras for an infinitary essentially algebraic theory, and can be presented by generators and relations. This result is combined with a general argument concerning categories of commutative monoids to give a very short proof of the localic Tychonoff Theorem.

It is also shown how frames can be presented as preframes, a result analogous to Johnstone's construction of frames from sites, and an application is given.

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Author information

Authors and Affiliations

  1. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, CB2 1SB, Cambridge

    Peter Johnstone

  2. Department of Computing, Imperial College, 180 Queen's Gate, SW7 2BZ, London

    Steven Vickers

Authors
  1. Peter Johnstone
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  2. Steven Vickers
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Editor information

Aurelio Carboni Maria Cristina Pedicchio Guiseppe Rosolini

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© 1991 Springer-Verlag

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Johnstone, P., Vickers, S. (1991). Preframe presentations present. In: Carboni, A., Pedicchio, M.C., Rosolini, G. (eds) Category Theory. Lecture Notes in Mathematics, vol 1488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084221

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  • DOI: https://doi.org/10.1007/BFb0084221

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54706-8

  • Online ISBN: 978-3-540-46435-8

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