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Is there a word to describe the process of making something categorical? “Categoricalization”?
By this I don’t mean a categorification, which is instead something “one level up”, I mean rather something like, for example, going to set theory to the category of sets and functions.
I suggest ’to make something categorical’. You said it yourself!
I think I’ve seen “categorization”.
… perhaps, but I think that “categorization” has also a separate meaning, namely something akin to ’putting the objects of study into categories’ (in this setting ’categories’ being almost synonymous to ’classes’ so the term would be analogous to ‘classification’ in that use.)
Isn’t “going from set theory to the category of sets and functions” a process of “putting the objects of study into categories”? (-:
Mike, I think Tim means ’categories’ in the common sense of the word, not mathematical. But I may be wrong here.
My reading of Mike’s #5 is that he had in mind both senses.
I haven’t yet found (through Google) confirmation of Mike’s #3, although if you look at the Idea section of category theory, under Examples, you see the use of the word “categorize”, effectively amalgamating these two senses. So I think “categorization” is apt; linguistically I much prefer it to the ungainly “categoricalization”.
I've seen this described as making things arrow-theoretical.
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