TY - JOUR
T1 - Functors on the category of quasi-fibrations
AU - Iwase, Norio
AU - Sakai, Michihiro
N1 - Funding Information:
E-mail addresses: iwase@math.kyushu-u.ac.jp (N. Iwase), sakai@kurume-nct.ac.jp (M. Sakai). 1 Supported by the Grant-in-Aid for Scientific Research #15340025 from Japan Society for the Promotion of Science.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2008/7/1
Y1 - 2008/7/1
N2 - We consider the following questions: when can we extend a continuous endofunctor on Top the category of topological spaces to a fibrewise continuous endofunctor on Top (2) the category of continuous maps? If this is true, does such fibrewise continuous endofunctor preserve fibrations? In this paper, we define Fib the topological category of cell-wise trivial fibre spaces over polyhedra and show that any continuous endofunctor on Top induces a fibrewise continuous endofunctor on Fib preserving the class of quasi-fibrations.
AB - We consider the following questions: when can we extend a continuous endofunctor on Top the category of topological spaces to a fibrewise continuous endofunctor on Top (2) the category of continuous maps? If this is true, does such fibrewise continuous endofunctor preserve fibrations? In this paper, we define Fib the topological category of cell-wise trivial fibre spaces over polyhedra and show that any continuous endofunctor on Top induces a fibrewise continuous endofunctor on Fib preserving the class of quasi-fibrations.
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U2 - 10.1016/j.topol.2008.04.001
DO - 10.1016/j.topol.2008.04.001
M3 - Article
AN - SCOPUS:44449087516
VL - 155
SP - 1403
EP - 1409
JO - Topology and its Applications
JF - Topology and its Applications
SN - 0166-8641
IS - 13
ER -