TY - JOUR
AU - Seymour, R. M.
AB - R. M. SEYMOUR 1. In this note we recall a general categorical construction due to May ([5, §12]) and use it to show how to construct such gadgets as functorial localizations and completions of (G-nilpotent) G-spaces, where G is a compact Lie group. Localizations and completions functorial up to homotopy were constructed and characterized by May, McClure and Triantafillou ([7, 8]). Ou r construction also gives a functorial approximation (up to weak G-homotopy equivalence) of any G-space by a G-CW-complex. Such an approximation, functorial up to homotopy, was given by Waner ([12]). Throughout we shall work in the category °U of compactly generated, weak Hausdorff spaces. In the nonequivariant setting, it is a maxim that functorial constructions are often easier to perform in the category of simplicial sets, and can then be converted into functorial constructions on spaces by means of the singular complex and geometric realization functors. For finite groups G this strategy directly generalizes to the equivariant setting. For general compact Lie groups G, however, passage through the category of simplicial sets results in loss of the G-action. Nevertheless, we shall prove a precise equivariant version of this maxim. Let K be a functor from simplicial sets 
TI - Some Functorial Constructions on G‐Spaces
JF - Bulletin of the London Mathematical Society
DO - 10.1112/blms/15.4.353
DA - 1983-07-01
UR - https://www.deepdyve.com/lp/wiley/some-functorial-constructions-on-g-spaces-NdcH5rmx4z
SP - 353
EP - 359
VL - 15
IS - 4
DP - DeepDyve
ER -