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- Title
The Homotopy Theory of Inverse Semigroups.
- Authors
Lawson, Mark V.; Matthews, Joseph; Porter, Tim; Margolis, S.
- Abstract
We show that abstract homotopy theory cain be used to define a suitable notion of homotopy equivalence for inverse semigroups. As an application of our theory, we prove a theorem for inverse semigroup homomorphisms which is the exact counterpart of the well-known result in topology which states that every continuous function cain be factorized into a homotopy equivalence followed by a fibration. We show that this factorization is isomorphic to the one constructed by Steinberg in his "Fibration Theorem", originally proved using a generalization of Tilson's derived category.
- Subjects
HOMOTOPY groups; INVERSE semigroups
- Publication
International Journal of Algebra & Computation, 2002, Vol 12, Issue 6, p755
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196702001061