It was argued by Crans that it is too much to ask that the category of Gray-categories admit a well behaved monoidal biclosed structure. We make this precise by establishing undesirable properties that any such monoidal biclosed structure must have. In particular we show that there does not exist any tensor product making the model category of Gray-categories into a monoidal model category.
Keywords: Gray-category, monoidal biclosed category, cocategory
2010 MSC: 18D05, 18D15, 18D35
Theory and Applications of Categories, Vol. 30, 2015, No. 11, pp 387-409.