You can find the strict version of that result in Prop. 1.4 of - M. Grandis, Homotopical algebra in homotopical categories, Appl. Categ. Structures 2 (1994), 351-406. I do not know if it has been written down elsewhere. For sure, whiskering of natural transformations with functors is used in: - R. Street, Categorical structures, in: Handbook of Algebra, Vol. 1, 529-577, North Holland, Amsterdam 1996. where you can find the notion of a sesqui-category (which does not assume the "reduced interchange axiom" you are mentioning). With best regards M. Grandis
Does anyone know of a reference for the following definition of a bicategory? The primitive composites are:
gf for composable 1-cells GF for vertically composable 2-cells f*G and F*g for horizontally composable pairs of each
with appropriate axioms including (G*f')(g*F)=(g'*F)(G*f), for F:f->f':X->Y and G:g->g':Y->Z. The horizontal composite G*F is defined to be the common value of the two vertical composites.
-Susan