The category of finite sets and Cartesian closed categories

Some universal properties of the category of finite sets with regard to Cartesian closed categories were studies. The equality of any two canonical morphisms (see Mac Lane[11]) in all Cartesian closed categories is redused to the equality of a finite number of maps in the category of finite sets. Hense, a new decision algorithm for equality of canonical morphisms has been obtained. Another, result is an algorithm to decide if two ($\&$, $\supset$)-formulas $A$ and $B$ are isomorphous in all Cartesian closed categories for any values of object-variables (where $\&$ is a cartesian product and $\supset$ is an internal hom-functor). The category of finite sets is used to prove the correctness of this algorithm.