I've finally been dipping into A=B lately and looking at the section on W-Z pairs, dual identities, and the like. I'm wondering if there are any sensible ways of interpreting that process combinatorially / categorically: essentially, can we go from a 'combinatorial interpretation' of one identity (possibly via Joyal's combinatorial species, etc.) to a combinatorial interpretation of its dual or one of its associated identities? If we have a functorial interpretation of some combinatorial identity, does the W-Z duality process correspond to a natural transformation into a functorial interpretation of the dual?
I've done a little digging and found some papers on categorical interpretations of hypergeometric series, but the approaches I've seen there feel a little unnatural; the groupoid interpretation of $1/n$ makes sense to me, but then the way they compose them to form hypergeometric series feels a lot like just 'multiplying out' rather than really finding natural interpretations of the series proper.
Any pointers to the literature on this, or even a good place to look for more on the relationships between the various transforms from A=B and combinatorial species, would be greatly appreciated!