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Removed the ’not for the adjective mealy’, as I felt it to be unnecessary and jar a bit!
Also changed the page name to the singular.
There is lots more that can be added to this page, e.g. how a Meely morphism determines a profunctor, a precise definition, a precise characterisation of when a profunctor determines a Meely morphism, etc. (As discussed in #21 and following here, the page is not quite correct at the moment.)
My immediate thought on reading the page was that in fine category theory tradition (cf prone, supine, wavy, etc) someone had decided to talk about mealy morphisms, and capitalised the word as a stylistic thing. But i guess the page doesn’t need both ’named for this guy Mealy’ and ’but not this other thing’ warnings.
But i guess the page doesn’t need both ’named for this guy Mealy’ and ’but not this other thing’ warnings.
Yes, exactly, we do not need both I think, but very good to clarify the etymology by including the first one :-).
Actually, I thought they were named after Mealy machines. (Which in turn were named after George Mealy, but there’s an extra step in the chain.)
Well, that’s true, I suppose.
Added some more references. In particular, I’ve made a note mentioning that Mealy morphisms are the same as “two-dimensional partial maps” due to Lawvere, however I cannot find an original reference for this statement. Street and Lack mention the reference
but I don’t suppose there are any written notes from this lecture series.
In the future I will add an actual definition of Mealy morphism and continue to expand the page.
Added the definition of Mealy morphism between enriched categories from the Paré paper.
I also removed some references to works of mine, where I refer to something as an example of a Mealy morphism that does not satisfy an additional constraint in the Pare paper that a certain functor be objectwise constant on fibres.
I will come back later to write a more accurate Idea section for this page.
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