Analogues of the Brown-van Kampen Theorem are considered. In particular profinite versions of CW-complexes
(1-CW complexes being interpretable as profinite graphs), fundamental groupoids, homotopies (weak) equivalences
will be introduced in order to perform such a task. At the same time more general projective limit techniques will
be investigated. connected with interest in fundamental group(oid)s of spaces glued from infinitely many
components.