The following preprint is available: M. Grandis "On the monad of proper factorisation systems in categories" (8 pages). Abstract. It is known that factorisation systems in categories can be viewed as unitary pseudo algebras for the "squaring" monad P = (-)^2, in Cat. We show in this note that an analogous fact holds for proper (i.e., epi-mono) factorisation systems and a suitable quotient of the former monad, deriving from a construct introduced by P. Freyd for stable homotopy. Some similarities of P with the structure of the path endofunctor of topological spaces are considered. Available in ps (148 K), from: ftp://pitagora.dima.unige.it/WWW/FTP/GRANDIS/EMfs.Jan01.ps Also in ps.gz (45K), at: http://arXiv.org/abs/math.CT/0101154 *** Marco Grandis Dipartimento di Matematica Universita' di Genova via Dodecaneso 35 16146 GENOVA, Italy http://www.dima.unige.it/STAFF/GRANDIS/