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On embedding categories in groupoids

Published online by Cambridge University Press:  01 September 2008

P. T. JOHNSTONE
P. T. JOHNSTONE*
Affiliation:
Department of Pure Mathematics, University of Cambridge, England.
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Abstract

We provide a new, unified approach to the necessary and sufficient conditions found by Mal'cev (1939) and by Lambek (1951) for embeddability of a semigroup in a group, and also show that each provides a necessary and sufficient set of conditions for the embeddability of a category in a groupoid. We show that all such conditions, and more besides, may be derived in a uniform way from a particular class of directed graphs which we call quadrangle clubs, and we prove a number of results (extending those of Mal'cev, Lambek, Bush and Krstić) on which families of quadrangle clubs provide sufficient conditions for embeddability.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 2 , September 2008 , pp. 273 - 294
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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