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Thanks for your recent edits, and in particular for looking into starting a page of this kind here, which has long been missing.
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Just for the record I’ll voice my usual complaint about terminology:
The word “categorical” means: without exceptions or conditions; absolute; unqualified; unconditional.
This is of course not what is meant here.
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In the present context the correct adjective is instead: “category-theoretic”.
A better title for this entry would be, in my opinion: category theoretic probability.
Now, I am aware that I am far outnumbered in holding this opinion.
Still, I feel that saying “categorical” for “category theoretic” is just wrong.
Just saying. Don’t let that stop you. Feel free to ignore me on this point.
If it’s of any use to you, Paolo, I have dumped a load of references here which at least are in nLab format.
Thank you, that’s very helpful!
Wasn’t there a convention to use “categorial” as the adjective for things related to category theory?
use “categorial” as the adjective for things related to category theory?
In ordinary English language there seems to be no real difference in meaning between “categorical” and “categorial”; cf. e.g. English.StackExchange/a/519672 (?)
(Also in German, for example, there are not even two such distinct words available, there is only kategorisch.)
But since “categorial” seems not to be used much in common speaking, it might at least be a better choice than “categorical” if one insists on abusing common terminology in the first place.
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(For what purpose, though? “category-theoretic” is precise, pronounced, and shorter than “categori(c)al approach”. Categories in themselves are not noteworthy; it is the theory of categories that usefully informs other fields like, in the present case, probability theory. If terminology can reflect that, it should.)
Changed the title to “category-theoretic”. All of you are making good points, and there’s also the additional point that “categorical random variables” in probability means “with values in a discrete set rather than real numbers”. And I want to avoid all possible confusion, we do consider real numbers here.
All right, thanks!
May I still lobby for shortening it to category-theoretic probability? :-)
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