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.