THE HOMOTOPY THEORY OF INVERSE SEMIGROUPS
2002 ◽
Vol 12
(06)
◽
pp. 755-790
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Keyword(s):
The One
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We show that abstract homotopy theory can 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 can 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.
2001 ◽
Vol 44
(3)
◽
pp. 549-569
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Keyword(s):
1977 ◽
Vol 18
(2)
◽
pp. 199-207
◽
1996 ◽
Vol 06
(05)
◽
pp. 541-551
1994 ◽
Vol 05
(03)
◽
pp. 349-372
◽
2016 ◽
Vol 94
(3)
◽
pp. 457-463
◽
1978 ◽
Vol 19
(1)
◽
pp. 59-65
◽
Keyword(s):