Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1403-1409 |
| Number of pages | 7 |
| Journal | Topology and its Applications |
| Volume | 155 |
| Issue number | 13 |
| DOIs | |
| Publication status | Published - Jul 1 2008 |
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All Science Journal Classification (ASJC) codes
- Geometry and Topology
Cite this
Functors on the category of quasi-fibrations. / Iwase, Norio; Sakai, Michihiro.
In: Topology and its Applications, Vol. 155, No. 13, 01.07.2008, p. 1403-1409.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Functors on the category of quasi-fibrations
AU - Iwase, Norio
AU - Sakai, Michihiro
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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UR - http://www.scopus.com/inward/citedby.url?scp=44449087516&partnerID=8YFLogxK
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 -