On embedding categories in groupoids

• Autores: P. T. Johnstone
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 2, 2008, págs. 273-294
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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 Krstic) on which families of quadrangle clubs provide sufficient conditions for embeddability.