Figure 6.

What are hom sets and hom functors? (a) A hom set, homQ (A, B), is a set of arrows from Apple (A) to Berry (B) in category Q. homQ (A, B) includes our familiar arrow, “nearly indistinguishable in color” but also many other different arrows (e.g. “indistinguishably tasty,” “indistinguishably sour,” etc). (b) A hom functor, hA, maps objects B and C in category Q into objects hA(B) and hA(C) in category Set. (c) hA also maps an arrow f in category Q into an arrow in category Set. (d) Visual depiction of hA: all sets of arrows emanating from A; and Ah: all sets of arrows pointing to A