In Memoriam

Abstract

1971 he moved to the University of Bremen where he was a full professor until he retired in 2002. Horst's mathematical work ranges over a large body of material, mostly in Topology, Algebra and Category Theory.In Category Theory he can be seen as the father of Categorical Topology, a beautiful field which inspired so many other researchers, and the genesis of which could already be seen in his monumental work "Topologische Reflexionen und Coreflexionen" which appeared in the Springer Lecture Notes in 1968. Starting in the seventies and throughout his career he developed the fundamentals of Categorical Topology, including topological functors, initial and final completions, factorization structures, cartesian closedness of topological constructs, and natural extensions. He also focused on the intuitive concept of nearness between arbitrary collections of sets, thus axiomatizing some new foundation for topology which he, together with one of his co-authors H. L. Bentley, proved to be extremely useful in the study of extensions of spaces.His visits to the U.S. near the end of the 60's and his collaboration with G. E. Strecker culminated in 1973 in the joint book "Category theory" which was very influential in the field. Later in the eighties together with J. Adámek the book was extended to "Abstract and Concrete Categories". This book has the subtitle "The Joy of Cats", reflecting Horst's humour and love for both categories and cats. It differs from other books in the field by emphasising concrete categories because of their importance for applying categorical methods to topological problems, and became "the" reference work for generations of researchers and students working in Categorical Topology.In the beginning of the eighties he published a paper entitled "Categorical Topology 1971-1981" with 700 references and containing many open problems. Together with