Have categories that are equipped with a faithful functor to some group (or perhaps monoid) ever been singled out as objects of study? I am especially interested in the use they might be put to as a categorical framework for quasiperiodicity. Here is the sort of thing I have in mind. Consider the Euclidean plane decorated with a particular Penrose tiling. For definiteness, regard the tiling as the characteristic function of the union of the edges of all the tiles. Consider the category C whose objects are non-empty open subsets of the plane such that given objects U and V, Hom(U,V) consists of functions f:U --> V which are restrictions of rigid motions of the plane and which commute with the tiling. Then there is a forgetful functor from C to the group of rigid motions of the plane. David Feldman Department of Mathematics University of New Hampshire ==============================================================================