  It is shown how double categories provide a direct abstract approach to
coloured operads; namely, product-preserving normal lax functors from (Pb C)^op
(the opposite of the double category of pullback squares in C) to Cat (the
double category of functors and profunctors) can be seen as generalized
operads, the standard ones arising when C = Set_f. In this context, generalized
symmetric monoidal categories are considered, in particular those arising from
indexed categories with sums or products.
