Title: Arrow Categories of Monoidal Model Categories,
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.