We define a mapping space for Gray-enriched categories adapted to higher gauge theory. Our construction differs significantly from the canonical mapping space of enriched categories in that it is much less rigid. The two essential ingredients are a path space construction for Gray-categories and a kind of comonadic resolution of the 1-dimensional structure of a given Gray-category obtained by lifting the resolution of ordinary categories along the canonical fibration of GrayCat over Cat.
Keywords: Higher gauge theory, Gray-categories
2010 MSC: primary: 18D05, 18D20; secondary: 55Q15
Theory and Applications of Categories, Vol. 29, 2014, No. 5, pp 100-187.