Denote "the" category of sets and functions by S. The hom set of functions from set X to set Y is denoted by S(X,Y). If C is a cartesian closed category denote by C(x,y) the set of morphisms from x to y in C. In such a C there exists a natural bijection between C(x,y) and C(1,y^x). In a sense, y^x reifies inside C the set C(x,y) in S. Both S(1,C(x,y)) and C(1,y^x) are sets, and in particular, if x=1, then both S(1,C(1,y)) and C(1,y^1) are sets. Anyhow, how does the "external" law of composition C(x,y) x C(y,z) ---> C(x,z) in S of C relate to the "internal" law of composition y^x x z^y ---> z^x in C? In summary, does the internal composition "reify" the external composition?