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On the homotopy theory of monoids

Part of: Applied homological algebra and category theory Semigroups

Published online by Cambridge University Press:  09 April 2009

Carol M. Hurwitz
Carol M. Hurwitz
Affiliation:
William Paterson CollegeDepartment of Mathematics, Wayne, New Jersey 07470, U.S.A.
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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.

MSC classification

Secondary: 20M50: Connections of semigroups with homological algebra and category theory 55U35: Abstract and axiomatic homotopy theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 2 , October 1989 , pp. 171 - 185
Copyright
Copyright © Australian Mathematical Society 1989

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