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U.W. Bangor - School of Informatics
Mathematics Preprints 2003

Semigroup and Automata Theory


03.10 : LAWSON, M.V. & STEINBERG, B.

Ordered groupoids and etendues

Summary:

Kock and Moerdijk proved that each etendue is generated by a site in which every morphism is monic. In this paper we provide an alternative characterisation of etendues in tems of ordered groupoids. Specifically, we define an Ehresmann site to be an ordered groupoid equipped with what we term an Ehresmann topology - this is essentially a family of order ideals closed under conjugation - and in this way we are able to define the notion of a sheaf on an Ehresmann site. Our main result is that each etendue is equivalent to the category of sheaves on a suitable Ehresmann site.

Published in:

Cahiers 45 (2004) 82-108.

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gzipped postscript files: 03_10l.ps.gz (long), 03_10s.ps.gz (short).


03.11 : LAWSON, M.V.

One-dimensional tiling semigroups

Summary:

Published in:

Semigroup Forum 68 (2004) 159-176.

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gzipped postscript file: 03_11.ps.gz


03.12 : LAWSON, M.V.

Ordered groupoids and left cancellative categories

Summary:

Published in:

Semigroup Forum 68 (2004) 458-476.

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gzipped postscript file: 03_12.ps.gz


03.13 : LAWSON, M.V.

Mosaics

Summary:

Published in:

Download:

gzipped postscript file: 03_13.ps.gz


03.14 : KELLENDONK, J. & LAWSON, M.V.

Universal groups for point-like sets and tilings

Summary:

Published in:

J. Algebra 276 (2004) 462-492.

Download:

gzipped postscript file: 03_14.ps.gz


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