PRO-C COMPLETIONS OF CROSSED-MODULES

Crossed modules occur in the theory of group presentations, in group cohomology and in providing algebraic models for certain homotopy types. There are profinite analogues of each of these contexts. In this paper, we examine the problem of extending the profinite completion functor on groups to one on crossed modules thus providing a method for comparing the information contained in profinite and abstract crossed modules in each of these situations. © 1990, Edinburgh Mathematical Society. All rights reserved.