#
Several constructions for factorization systems

##
Dali Zangurashvili

The paper develops the previously proposed approach to
constructing factorization systems in general categories. This
approach is applied to the problem of finding conditions under which
a functor (not necessarily admitting a right adjoint) `reflects'
factorization systems. In particular, a generalization of the well-known
Cassidy-Héebert-Kelly factorization theorem is given. The problem
of relating a factorization system to a pointed endofunctor is considered.
Some relevant examples in concrete categories are given.

Keywords:
(local) factorization system, family of adjunctions between
slice categories, semi-left-exact reflection, fibration, (co)pointed
endofunctor

2000 MSC:
18A20, 18A32, 18A25

*Theory and Applications of Categories,*
Vol. 12, 2004,
No. 11, pp 326-354.

http://www.tac.mta.ca/tac/volumes/12/11/12-11.dvi

http://www.tac.mta.ca/tac/volumes/12/11/12-11.ps

http://www.tac.mta.ca/tac/volumes/12/11/12-11.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/12/11/12-11.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/12/11/12-11.ps

TAC Home