Iterated Monoidal Categories

We develop a notion of iterated monoidal category and show that this notion corresponds in a precise way to the notion of iterated loop space. Specifically the group completion of the nerve of such a category is an iterated loop space and free iterated monoidal categories give rise to finite simplicial operads of the same homotopy type as the classical little cubes operads used to parametrize the higher H-space structure of iterated loop spaces. Iterated monoidal categories encompass, as a special case, the notion of braided tensor categories, as used in the theory of quantum groups.Comment: 55 pages, 3 PostScript figure

Strong Cofibrations and Fibrations in Enriched Categories

We define strong cofibrations and fibrations in toplogically enriched categories using the relative homotopy extension resp. lifting property. We prove a general pairing result, which for topological spaces specializes to the well-known product theorem for cofibrations. Strong cofibrations and fibrations give rise to cofibration and fibration categories in the sense of homotopical algebra. Finally we discuss the preservation of such maps under various forgetful functors of categories of highly structured spectra

MacLane homology and topological Hochschild homology

Fiedorowic Z, Pirashvili T, Schwänzl R, Vogt RM, Waldhausen F. MacLane homology and topological Hochschild homology. Mathematische Annalen. 1995;303(1):149-164

Harvesting Mathematics

By the end of March 1996, nearly all mathematics departments in the FRG were present on the WWW. Difficulties arise with navigating, due to the relatively high number of servers. We discuss "Harvest" as a useful, useable, and scalable aid to documentation. Included is a description of a sample installation indexing preprints and a few proposals on how to upgrade query output. 1 Introduction WWW servers are publication media. They represent a new type of media comparable to the introduction of letterpress printing. Letterpress printing allowed the production of a large number of copies of some written work for the first time. What remained necessary for the duplication and distribution of a work was a considerable amount of organization and technical work which could not be carried out by the author. It became deferred to the publishers. They also were used in mathematics as switchboards for quality control. The use of WWW servers creates massive changes: ffl The duplication of a math..

Topological Hochschild Homology

Schwänzl R, Vogt RM, Waldhausen F. Topological Hochschild Homology. Journal of the London Mathematical Society (2). 2000;62(2):345-356