Adamek and Sousa recently solved the problem of characterizing
the subcategories *K* of a locally $\lambda$-presentable category
*C* which are $\lambda$-orthogonal in *C*, using their concept
of *K*$\lambda$-pure morphism. We strengthen the latter
definition, in order to obtain a characterization of the classes
defined by orthogonality with respect to $\lambda$-presentable
morphisms (where $f : A \rightarrow B is called
$\lambda$-presentable if it is a $\lambda$-presentable object of
the comma category A/*C*). Those classes
are natural examples of reflective subcategories defined by proper
classes of morphisms. Adamek and Sousa's result follows from
ours. We also prove that $\lambda$-presentable morphisms are
precisely the pushouts of morphisms between $\lambda$-presentable
objects of *C*.

Keywords: pure morphism, othogonality, injectivity, locally presentable categories, accessible categories

2000 MSC: 18A20, 18C35, 03C60, 18G05

*Theory and Applications of Categories,*
Vol. 12, 2004,
No. 12, pp 355-371.

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

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

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

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

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