Hans-Joachim Baues (-2020) was a German algebraic topologist.
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 homotopy theory:
Hans-Joachim Baues: Algebraic Homotopy, Cambridge studies in advanced mathematics 15, Cambridge University Press (1989)
Hans-Joachim Baues: Combinatorial Homotopy and 4-Dimensional Complexes, de Gruyter Expositions in Mathematics 2, Walter de Gruyter (1991)
Hans-Joachim Baues: Homotopy Type and Homology, Oxford University Press (1996) [ISBN:9780198514824, pdf]
Hans-Joachim Baues: Homotopy types, in: Ioan Mackenzie James (ed.) Handbook of Algebraic Topology, North Holland (1995) [doi:10.1016/B978-0-444-81779-2.X5000-7, ISBN:9780080532981]
(with Antonio Quintero) Infinite Homotopy Theory, K-monographs in mathematics 6 Kluwer (2001)
On cohomology of monoids in monoidal categories (specifically in distributive monoidal categories):
Last revised on January 3, 2026 at 15:54:47. See the history of this page for a list of all contributions to it.