for C being Category holds
( C is with_finite_product iff ( ex a being Object of C st a is terminal & ( for a, b being Object of C ex c being Object of C ex p1, p2 being Morphism of C st
( dom p1 = c & dom p2 = c & cod p1 = a & cod p2 = b & c is_a_product_wrt p1,p2 ) ) ) )