Arrow Categories of Monoidal Model Categories
Algebraic Topology
2024-05-27 v3 Algebraic Geometry
Category Theory
K-Theory and Homology
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, and has the important consequence that it allows for the consideration of a monoidal product in cubical homotopy theory. As illustrations we include numerous examples of non-cofibrantly generated monoidal model categories, including chain complexes, small categories, topological spaces, and pro-categories.
Keywords
Cite
@article{arxiv.1703.05359,
title = {Arrow Categories of Monoidal Model Categories},
author = {David White and Donald Yau},
journal= {arXiv preprint arXiv:1703.05359},
year = {2024}
}
Comments
13 pages. Comments welcome. Version 2 adds more examples, and an application to cubical homotopy theory. Version 3 is the final, journal version, accepted to Mathematica Scandinavica