Functorial reducing pro*-Grp category to pro-Grp

摘要

We introduce a new functor (R) over tilde from pro*-Grp to pro-Grp and use it to give a new characterisation of coarse shape groups. It is shown that lim o (R) over tilde o pro*-pi(k) = pi*(k), thus (R) over tilde o pro*-pi(k) is a full analogue of pro-pi(k). Furthermore, the Hurewicz theorem in a new context is proposed. We complete with a corollary stating isomorphicity of the first nontrivial coarse shape group and coarse shape homology group of a pointed continuum, assertion that does not hold for shape groups. (C) 2019 Elsevier B.V. All rights reserved.