Abstract
AbstractWe 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Mathematical Proceedings of the Cambridge Philosophical Society
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
