Full paper in PDF format:
$%I. Pop and A. Tofan, Cofibrations and bicofibrations
for -algebras, Rev. Mat. Complut. 21 (2008), no. 2, 529–552.%$
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ABSTRACT
The paper deals with the correlated concepts of cofibration and bicofibration
in -algebra theory. We study cofibrations of
-algebras introduced by
Claude Schochet in (Claude Schochet, Topological methods for
-algebras, III: Axiomatic homology, 1984) [see also (C.
Mohorianu and I. Pop, On the existence of some homotopy commutative
diagrams of *-homomorphisms, 2007)]. Cofibrations are characterized by means
of the mapping cylinder
-algebras. We also define and analyze the notion
of bicofibration for
-algebras based on the topological model from (I. Pop,
Bicofibrations, 1980) [see
also (R. W. Kieboom, A bicofibration is just a pair of strictly
separated cofibrations, 1983)]. As an application, an exact sequence of Čerin’s homotopy groups (Z.
Čerin, Homotopy groups for
-algebras, 1995), is
obtained.
Key words: -algebra, homotopic
-homomorphisms, cofibration (bicofibration)
of
-algebras, mapping cylinder (cone), double mapping cylinder, Čerin’s homotopy
groups for
-algebras.
2000 Mathematics Subject Classification: 46L85, 55P05.