It is proved that all the isomorphisms in the cartesian category freely generated by a set of objects (i.e., a graph without arrows) can be written in terms of arrows from the symmetric monoidal ...

G. A. Miller, Group of Isomorphisms of a Transitive Substitution Group, Proceedings of the National Academy of Sciences of the United States of America, Vol. 7, No. 12 (Dec. 15, 1921), pp. 325-328 ...