There are many things which can be computed (derived) from a context, some of which might be even hard (expensive) to compute (e.g., the stem base or the concept lattice). It could be useful (and save resources) if such items could be computed once and made available via the repository. That would also allow testing of algorithms.
One issue to consider is whether accepted file formats exist for the considered items.
My suggestion would be to store such information in separate directories, e.g., derivatives/lattices/, derivatives/bases, etc.