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Kalan Kucera (Apr 23 2022 at 00:29):If I am trying to create objects and morphisms within a general Cat of Empirical Models, and there are constants which scale the resultant data, do the constants belong in the domain, or are they scalars for the morphisms translating my independent variables to the codomain? (If any of that makes sense)
Morgan Rogers (he/him) (Apr 23 2022 at 10:15):I don't know what the objects or morphisms of your empirical model category are, but from what I understand of your question: if the scaling represents a valid transformation of models then they're likely endomorphisms, not living "in" the domain but as arrows from the domain to itself. If you are talking about scaling the output of a transformation, then this is again going to produce more arrows rather than living "in" the objects. Either way, if the morphisms between pairs of objects have some structure (like scaling by scalars in some fixed ring) which is compatible with composition, then you might want to consider an enriched category.
Notification Bot (Apr 26 2022 at 08:41):This topic was moved here from #theory: category theory > constants in empirical models by Matteo Capucci (he/him).