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Idem for Mealy machines to link with Mealy morphism
I am having a silly problem with the links to Moore machines. One of the links works perfectly, the other two just come out as text. (I’m probably doing something silly, but cannot see what it is.)
Thanks for fixing that! Doh!
It may be worthwhile adding more on this automata theoretic stuff, but I’m not sure what would make sense to add. The link with higher dimensional automata might be feasible but is not that obvious.
Looking at this entry, I would find it difficult to write down an explicit definition of a Mealy morphism. I think it could be done but I would not be certain if I got it right or not! I do not have access to Bob Paré’s original as it is behind a paywall. Could some kind person add the definition to the entry?
This is really just for completeness as I do not intend to work on this myself. It would also be great if someone included the conceptual link between Mealy morphisms and Mealy machines as well and to ask a dumb question, is there some link between morphisms of Mealy machines as defined in the coalgebraic context and notions here?
have touched the formatting of the traditional component definition (here)
added a remark (here) translating to the more compact definitions of effectful maps
(after some searching I still don’t find a citable reference which says this really well: The author of github.com/orakaro/MonadicMealyMachine has it right, but all other authors I found who at least think about currying $I \times S \to O \times S$ curry it as $S \to [I, S \times O]$ instead of the more natural $I \to [S, S \times O]$.)
Won’t anyone speaking of the Kleisli category of the state monad count? Such as here p. 462.
Thanks for joining in – but the text logic is broken now:
The remark titled (by me) “Mealy machines as effectful maps” is now re-filled with material that says nothing at all about effectful maps.
The half of my lead-in sentence which you retained, advertizing a “more concise” formulation, is contradicted by your definition of “$Mly(-)$” which is everything but more concise. In fact it’s hard to see what it has to do with Mealy machines, and I’d please urge you to add explanation of why one would want to make this definition.
But first, I’ll restore my latest version of the entry now and then append the material you added to the end of that.
So I have moved your material to its own subsection, now here
and added pointer to the preprints that it is taken from:
Prop. 3.5 in
and Def. 2.1 in:
I have also polished up the typesetting a little.
Finally I prefixed the pullback-definition of $Mly$ with a couple of paragraphs on regarding Mealy machines as spans.
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