Preprints available

[categories <cat-dist@mta.ca>]

Date: Tue, 5 Aug 1997 17:19:51 -0400
From: Walter Tholen <tholen@mathstat.yorku.ca>

The following two preprints (joint work with George Janelidze) are available as
postscript files from my home page at
http://www.math.yorku.ca/Who/Faculty/Tholen/menu.html
For titles and abstracts, see below.

Walter Tholen

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"Functorial Factorization, Well-pointedness and Separabilty"

Abstract: A functorial treatment of factorization structures is presented,
under extensive use of well-pointed endofunctors. Actually, so-called weak
factorization systems are interpreted as pointed lax indexed endofunctors,
and this sheds new light on the correspondence between reflective subcategories
and factorization systems. The second part of the paper presents two improtant
factorization structures in the context of pointed endofunctors:
concordant-dissonant and inseparable-sepaprable.


"Extended Galois Theory And Dissonant Morphisms"

Abstract: For a given Galois structure on a category C and an effective descent
morphism p: E --> B in C we describe the category of so-called weakly split
objects over (E,p) in terms of internal actions of the Galois (pre)groupoid of
(E,p) with an additional structure. We explain that this generates various
known results in categorical Galois theory and in particular two results of M.
Barr and R. Diaconescu. We also give an elaborate list of examples and
applications.