In hopes that we can finally get a useful (e.g., correct but not tautological) description of the finitely presentable set-valued functors on a small category : Note that if there were no non-representable quotients of representables on Delta, then loops, spheres, etc would be more difficult to locate. While a non-singular figure can be defined as any monomorphism from a representable, "non-degenerate " figures can be singular since that is taken to mean that the only factorization with the first part a SPLIT epimorphism p has in fact that p is an isomorphism. In other words, since we assume the small category to be Karoubi-complete, a degenerate figure is one which is fixed by some non-trivial idempotent incidence relation. Any subcategory of the small category gives rise to an essential subtopos, i.e., to a left adjoint to the restriction functor, which when composed with that restriction yields a cocontinuous idempotent comonad which may be called the n-skeleton where n is the subcategory. Conjecture : For small a category with finite hom-sets, a set-functor is fp iff it has finite values and is n-skeletal for some finite n.