A note on model (co)slice categories

Abstract

There are various adjunctions between model (co)slice categories. The author gives a proposition to characterize when these adjunctions are Quillen equivalences. As an application, a triangle equivalence between the stable category of a Frobenius category and the homotopy category of a non-pointed model category is given.

Keywords

Model slice categories / Homotopy categories / Quillen equivalences

References

[1] Dwyer W. G., Spalinski J.. James I. M.. Homotopy Theories and Model Categories, Handbook of Algebraic Topology. Elsevier Science B.V., 1995

[2] Gillespie J.. Model structures on exact categories. J. Pure Appl. Algebra, 2011, 215: 2892-2902

[3] Happel, D., Triangulated Categories in the Representation Theory of Finite-Dimensional Algebras, London Math. Soc. Lecture Note Series, Vol. 119, Cambridge University Press, Cambridge, 1988.

[4] Hirschhorn, P. S., Model Categories and Their Localizations, Mathematical Surveys and Monographs, Vol. 99, Amer. Math. Soc., Providence, RI, 2003.

[5] Hovey, M., Model categories, Mathematical Surveys and Monographs, Vol. 63. Amer. Math. Soc., Providence, RI, 1999.

[6] Maclane, S., Categories for the Working Mathematician, Grad. Texts in Math., Vol. 5, Springer-Verlag, New York, 1971.

[7] May J. P., Ponto K.. More concise Algebraic Topology: Localization, Completion, and Model Categories. Chicago Lectures in Math., 2012, Chicago, IL: University of Chicago Press

[8] Quillen, D. G., Homotopical Algebra, Lect. Notes in Math., Vol. 43, Springer-Verlag, Berlin, 1967.