Fibrations in the Category of Absolute Neighborhood Retracts

Takahisa Miyata. "Fibrations in the Category of Absolute Neighborhood Retracts." Bulletin of the Polish Academy of Sciences. Mathematics 55.2 (2007): 145-154. <http://eudml.org/doc/280392>.

@article{TakahisaMiyata2007,
abstract = {The category Top of topological spaces and continuous maps has the structures of a fibration category and a cofibration category in the sense of Baues, where fibration = Hurewicz fibration, cofibration = the usual cofibration, and weak equivalence = homotopy equivalence. Concentrating on fibrations, we consider the problem: given a full subcategory 𝓒 of Top, is the fibration structure of Top restricted to 𝓒 a fibration category? In this paper we take the special case where 𝓒 is the full subcategory ANR of Top whose objects are absolute neighborhood retracts. The main result is that ANR has the structure of a fibration category if fibration = map having a property that is slightly stronger than the usual homotopy lifting property, and weak equivalence = homotopy equivalence.},
author = {Takahisa Miyata},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {ANR; fibration category; strong homotopy lifting property},
language = {eng},
number = {2},
pages = {145-154},
title = {Fibrations in the Category of Absolute Neighborhood Retracts},
url = {http://eudml.org/doc/280392},
volume = {55},
year = {2007},
}

TY - JOUR
AU - Takahisa Miyata
TI - Fibrations in the Category of Absolute Neighborhood Retracts
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2007
VL - 55
IS - 2
SP - 145
EP - 154
AB - The category Top of topological spaces and continuous maps has the structures of a fibration category and a cofibration category in the sense of Baues, where fibration = Hurewicz fibration, cofibration = the usual cofibration, and weak equivalence = homotopy equivalence. Concentrating on fibrations, we consider the problem: given a full subcategory 𝓒 of Top, is the fibration structure of Top restricted to 𝓒 a fibration category? In this paper we take the special case where 𝓒 is the full subcategory ANR of Top whose objects are absolute neighborhood retracts. The main result is that ANR has the structure of a fibration category if fibration = map having a property that is slightly stronger than the usual homotopy lifting property, and weak equivalence = homotopy equivalence.
LA - eng
KW - ANR; fibration category; strong homotopy lifting property
UR - http://eudml.org/doc/280392
ER -