J Austral Math Soc Ser A 47 pp171--185, 1989.

On the Homotopy Theory of Monoids

Carol M. Hurwitz

Abstract

In this paper, it is shown that any connected, small category can be embedded in a semi-groupoid (a category in which there is at least one isomorphism between any two elements) in such a way that the embedding includes a homotopy equivalence of classifying spaces. This immediately gives a monoid whose classifying space is of the same homotopy type as that of the small category. This construction is essentially algorithmic, and furthermore, yields a finitely presented monoid whenever the small category is finitely presented. Some of these results are generalizations of ideas of McDuff.

1980 AMS Subject Classification (1985 Revision): 20M50

Browse the article

Authors

Carol M. Hurwitz

William Paterson College, Department of Mathematics, Wayne, New Jersey 07470, U.S.A.