Categorical methods in topology, algebra and computer science

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Category theory aims at detecting common aspects of various mathematical theories and at establishing theorems that are therefore simultaneously applicable to many distinct areas of mathematics and its applications in the natural sciences, without necessarily resorting to traditional foundations based on set theory. The proposed project is concentrated on the interface between algebra and topology, but will also reach out to themes pursued in homotopical algebra, algebraic geometry, and domain theory. Specifically, we wish -  to study comprehensively so-called lax Eilenberg-Moore algebras, which are designed to make structures of general topology accessible to tools that have been successfully used in algebra, - to refine and extend the existing "intrinsic" theory of topological structures in rather arbitrary categories and apply it to the afore-mentioned lax algebras, - to develop a theory of torsion and of localizations that is applicable to semi-abelian categories and beyond, as well as to the triangulated categories of stable homotopy theory, - to establish a theory of lax factorization structures with the aim of applying it in homotopy theory, - to give a new treatment of categories of Chu spaces, in terms of their topologicity over the base category, and integrate them into Sambin's approach to formal topology as used in theoretical computer science.