Arrow categories of monoidal model categories

  • David White
  • Donald Yau

Abstract

We prove that the arrow category of a monoidal model category, equipped with the pushout product monoidal structure and the projective model structure, is a monoidal model category. This answers a question posed by Mark Hovey, in the course of his work on Smith ideals. As a corollary, we prove that the projective model structure in cubical homotopy theory is a monoidal model structure. As illustrations we include numerous examples of non-cofibrantly generated monoidal model categories, including chain complexes, small categories, pro-categories, and topological spaces.

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Published
2019-10-19
How to Cite
White, D., & Yau, D. (2019). Arrow categories of monoidal model categories. MATHEMATICA SCANDINAVICA, 125(2), 185-198. https://doi.org/10.7146/math.scand.a-114968
Section
Articles