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Strictness of two operations on proarrow equipments
The advantage of definition 2 is that the composition of profunctors is strictly associative/unital (just functor composition) whereas composition using definition 1 is only weakly associative/unital. … If we are interested in the pro-arrow equipment of categories/functors/profunctors/natural transformations, then we also use the operation of restriction of a profunctor $R : C \not\rightarrow D$ along …