Hans-Joachim Baues (d. May 8, 2020) was a German topologist and the author of

*Algebraic Homotopy*, Cambridge studies in advanced mathematics 15, Cambridge University Press, (1989);*Combinatorial Homotopy and 4-Dimensional Complexes*, de Gruyter Expositions in Mathematics 2, Walter de Gruyter, (1991);*Homotopy Types*, in I.M.James, ed.,*Handbook of Algebraic Topology*, 1–72, Elsevier, (1995);*Homotopy type and homology*, Oxford University Press, 1996- (with Antonio Quintero)
*Infinite Homotopy Theory*, K-monographs in mathematics, Volume 6, Kluwer, 2001;

among other works.

A part of his work developed the ideas of Whitehead's basic programme for algebraic homotopy, using a mix of cofibration categories and categories with a particular type of cylinder functor, that he called I-categories. These are treated in separate entries.

Baues also systematically developed aspects of secondary homological algebra (secondary cohomological operations, secondary Steenrod algebra, secondary chain complexes, secondary triangulated category) which is a form of categorification of the usual homological algebra. He developed them together to give sound applications in the computations with Adams-Novikov spectral sequence and calculations of homotopy groups of spheres.

He is also well known for his development of the “cohomology of small categories” with Wirsching, sometimes called Baues-Wirsching cohomology, although versions of this theory existed prior to his contribution.

On cohomology of monoids in monoidal categories (specifically in distributive monoidal categories):

- Hans-Joachim Baues, Mamuka Jibladze, Andy Tonks,
*Cohomology of monoids in monoidal categories*, in:*Operads: Proceedings of Renaissance Conferences*, Contemporary Mathematics**202**, AMS (1997) 137-166 [doi:10.1090/conm/202, preprint:pdf]

category: people

Last revised on June 4, 2023 at 14:27:20. See the history of this page for a list of all contributions to it.