categories: preprint: On the monad of proper factorisation systems in categories

[grandis@dima.unige.it (Marco Grandis)]

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/