I have made the following recent papers available from my home page at www.math.yorku.ca/~tholen I appreciate receiving any comments that you may have. Regards, Walter. ------------------------------------- Marco Grandis and Walter Tholen: Natural weak factorization systems Abstract. In order to facilitate a natural choice for morphisms created by the (left or right) lifting property as used in the definition of weak factorization systems, the notion of natural weak factorization system in the category K is introduced, as a pair (comonad, monad) over K^2. The link with existing notions in terms of morphism classes is given via the respective Eilenberg-Moore categories. ------------------------------------- Jiri Rosicky and Walter Tholen: Factorization, fibration and torsion Abstract. A simple definition of torsion theory is presented, as a factorization system with both classes satisfying the 3-for-2 property. Comparisons with the traditional notion are given, as well as connections with the notions of fibration and of weak factorization system, as used in abstract homotopy theory. ------------------------------------- Eraldo Giuli and Walter Tholen: A topologist's view of Chu spaces Abstract. For a symmetric monoidal-closed category X and any object K, the category of K-Chu spaces is small-topological over X and small-cotopological over X^op. It's full subcategory of M-extensive K-Chu spaces is topological over X when X is M-complete, for any morphism class M. Often they form a full coreflective subcategory of Diers' category of affine K-spaces. Hence, in addition to their roots in in the theory of pairs of topological vector spaces (Barr) and in the study of event structures for modeling concurrent processes (Pratt), Chu spaces seem to have a less explored link with algebraic geometry. We use the Zariski closure operator to characterize the self-dual category of M-extensive and M-coextensive K-Chu spaces.