A subshape spectrum for compacta

Nikica Uglesic
2005 Glasnik Matematicki - Serija III  
A sequence of categories and functors between them are constructed. They form a subshape spectrum for compacta in the following sense: Each of these categories classifies compact ANR's just as the homotopy category does; the classification of compacta by the "finest" of these categories coincides with the shape type classification; moreover, the finest category contains a subcategory which is isomorphic to the shape category; there exists a functor of the shape category to each of these
more » ... ch of these categories, as well as of a "finer" category to a "coarser" one; the functors commute according to the indices. Further, a few applications of the "subshape spectrum theory" are demonstrated. It is shown that the S * -equivalence (a uniformization of the Mardešić S-equivalence) and the q * -equivalence (a uniformization of the Borsuk quasi-equivalence) admit the category characterizations within the subshape spectrum, and that the q * -equivalence implies (but is not equivalent to) the S * -equivalence. 2000 Mathematics Subject Classification. 55P55, 18A32.
doi:10.3336/gm.40.2.15 fatcat:lvmxgmsyfnad7nbwaubpxzcxui