A new normal form for the compositions of morphisms and inverse morphisms

Abstract

It is shown that for every compositionτ of morphisms and inverse morphisms there exist morphismsh1,h2,h3, andh4 such that\(\tau = h_4^{ - 1} \circ h_3 \circ h_2^{ - 1} \circ h_1 \). This solves a problem raised by Latteux and Leguy [5] and partially solved by Turakainen [8], [9].