Notes on an Algebraic Stable Homotopy Category

  • Ryo KatoEmail author
  • Hiroki Okajima
  • Katsumi Shimomura
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 309)


Ohkawa showed that the collection of Bousfield classes of the stable homotopy category of spectra is a set (Ohkawa in Hiroshima Math. J. 19:631–639, [8]). Let \({\mathcal C}\) be an algebraic stable homotopy category in the sense of Hovey, Palmieri and Strickland (Axiomatic Stable Homotopy Theory, American Mathematical Society, Providence, RI, [6]). We here show that Bousfield classes of \({\mathcal C}\) form a set by introducing a homology theory based on the generators of \({\mathcal C}\), in a similar manner as Dwyer and Palmieri did in Dwyer and Palmieri (Proc. Am. Math. Soc. 129(3):881–886, [3]). We also consider a relation between Bousfield classes of finite objects and supports of them on a collection of objects.


Stable homotopy category Bousfield lattice Ohkawa theorem 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Faculty of Fundamental Science, National Institute of TechnologyNiihama CollegeNiihamaJapan
  2. 2.Department of Mathematics, Faculty of ScienceKochi UniversityKochiJapan

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