Concerning categories enriched in monoidal categories with a single object: another example is given by cocycles. It can be presented in various ways. For example, a "\v Cech style" version: given an open cover of X by Ui and a (suitably normalized) \v Cech 3-cocycle c of this cover with values in M, this enrichs in the evident way the category whose objects are the i's, with hom(i,j) either a singleton or empty according to inhabitedness of the intersection of Ui and Uj. Other variations suggest things like morphisms of simplicial sets to the nerve of M considered as a 2-category with a single 1-cell. This is related to K(M,2)-torsors, etc. Quite probably there are several publications exploiting this. At least cocycles with values in monoids rather than groups certainly have been considered. What I certainly have not seen is a backwards generalization: has anybody considered analogs of K(M,2)-torsors for general enrichments? Would be very interested in a reference. Happy holidays to all! Mamuka