Subject: categories: Manuscripts available

From: mhebert <[email-masked]>
Date: Tue, 03 Oct 2000 00:06:36 +0200

The following manuscripts are available on request, or can be downloaded in 
postscript form from
http://www.aucegypt.edu/schools/sse/maths/Staff/Hebert/HebertHomePage.htm

On abstract data types presented by multiequations
J.Adamek, M Hebert, J.Rosicky.

Abstract:
Equational presentation of abstract data types is generalized to presentation 
by multiequations, i.e., exclusive-or's of equations, in order to capture 
parametric data types such as array or set. Multiinitial-algebra semantics for 
such data types is introduced. Classes of algebras described by multiequations 
are characterized.

Uncountable orthogonality is a closure property
M.Hebert, J.Rosicky

Abstract:
We show that, for lambda-orthogonality classes in locally lambda-presentable 
categories coincide with full subcategories closed under limits and 
lambda-directed colimits. This comes as a surprise, since the statement is 
known to be false for lambda = omega.

More on orthogonality in locally presentable categories
M. Hebert, J. Adamek and J. Rosicky

Abstract:
A new solution of the orthogonal subcategory problem in locally presentable 
categories is exhibited, substantially different from the classical one of 
Gabriel and Ulmer.
It has various applications: we use it to characterize omega-orthogonality 
classes in locally finitely presentable categories, i.e., the full 
subcategories orthogonal to a set of morphisms the domains and codomains of 
which are finitely presentable. We also use it to find a sufficient condition 
for reflectivity of subcategories of accessible categories. And finally, we 
describe categories of fractions in all small, finitely complete categories.

Lambda*-injectivity + special lambda-compactness =  lambda-injectivity
Michel Hébert

Abstract:
J.Rosicky, J.Adamek and F.Borceux recently showed that lambda-injectivity 
classes in locally presentable categories are precisely the classes closed 
under products, lambda-filtered colimits and lambda-pure subobjects. We 
present a simpler and more conceptual proof of this result, obtaining it as a 
consequence of our characterization of lambda-injectivity classes (JPAA 129 
(1998) 143-147) and of an infinitary compactness result.