Categorical Algebra and its Applications

Francis Borceux is Professor of mathematics at the University of Louvain since many years. He has developed research in algebra and essentially taught geometry, number theory and algebra courses and he has been dean of the Faculty of Sciences of his University and chairman of the Mathematical Committee of the Belgian National Scientific Research Foundation.

Are all limit-closed subcategories of locally presentable categories reflective?.- On categories with effective unions.- Descent theory for Banach modules.- Pseudofunctors and non-abelian weak equivalences.- An exact sequence in the first variable for non-abelian cohomology in algebraic categories. A mayer-vietoris sequence for non-abelian cohomology of groups.- Locally hilbert categories.- Sur la convergence de suites de fonctions suivant des filtres.- The azumaya complex of a commutative ring.- The spectrum lattice of baer rings and polynomials.- Morse germs in S.D.G..- Modal and tense predicate logic: Models in presheaves and categorical conceptualization.- On the representability of partial morphisms in top and in related constructs.- Remarks on localic groups.- Weak products and Hausdorff locales.- Generalized fibre bundles.- Closure operators with prescribed properties.- On the unity of algebra and logic.- The cohomology groups of an epimorphism.- Decker's sharper Künneth formula.- On a categorical analysis of Zadeh generalized subsets of sets I.- Global and infinitesimal observables(?).- Toposes and groupoids.- Componental nuclei.- Representation theorems for P-categories.- On the category of compact convex sets and related categories.- Fillers for nerves.- Simultaneous representations in categories.- Uniform spaces can be represented by completely distributive lattices.