EricS, Thanks for getting back to me with a reference[1]. I printed a couple of pages of it, which I then scrape out time to read.
In a rare moment of straightforward computation, NickT walked me through how one performs an analysis of variation. Now I am reading a little bit of "Beyond Versus" about the history of the nature-nurture debate. There, the author discusses Fisher's notion of *interaction* as a deviation from additivity. This got me thinking again about my question regarding additivity and your comment about finding correct *aggregation operators*. To what degree does this *wider class* of operators correspond to instances of coproducts in context-appropriate categories? My wondering begins with the observation that *interactions* can often be represented by (hyper?)-arrows (or at least *(hyper?)-edges) and that such structured things can often have their own notions of *additivity* (following from the notion of coproduct and especially in linear categories, aka, additive categories). Does this jive with your understanding? [1] https://redfish.com/pipermail/friam_redfish.com/2022-April/092364.html
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