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Added quadrability of a cospan (and coquadrability of a span) as well as quadrability/coquadrability of a category C. The word "quadrable" means "squarable", but "squarable" isn't a real word. The word "quadrable" is the proper translation of the French "carrable".
Note that while the translation "quadrable" is uncommon, the term "carrable" in French is standard.
I edited the entry a bit:
added an Idea-section;
renamed the ambient category from to so that the symbol doesn’t collide with that for its objects, , , ;
linked to it from span and cospan, so that there is a chance that people find this entry.
It would be good if you could include a reference that uses the terminology “quadrable”.
I've only seen the term "carrable" in French (It's in Toen's cours 2 of Toen's notes for example, but if you search for it on google, you will find that it's standard terminology in french). The corresponding word in English is "quadrable" (according to the dictionary). If you want to change it to "squarable", then I don't mind that either, but "quadrable" is proper English, while "squarable" isn't.
I've seen "carrable" used in English as well, citing the French term, but there is no reason why we shouldn't translate it.
In conclusion, you can change the term to any of the three "quadrable", "squarable", or "carrable," although I prefer the first one, but I don't really care if you change it to what you prefer. I've provided a correct definition, and the page is complete enough for anyone who would look up the definition, so if you'd like to add anything else (or change the page), be my guest.
(Perhaps a redirect for carrable and squarable would be in order as well.)
In conclusion, you can change the term to any of the three “quadrable”, “squarable”, or “carrable,” although I prefer the first one.
I think the important thing is that we have this remark on terminology in the nLab entry. I’ll put it in there now.
I object to the use of the term presheaf category, because it is not taking values in sets.
okay, if you wish, I make it “functor category”.
I also made a mistake when I was changing around the page (in particular, in giving the map *_F, I forgot to add an ^op over Sp in the second [Sp,C] of the boxes(I had originally written everything dually)). I would fix it, but it seems like you're still editing it
I am done editing now (got distracted by something else in the middle of it). Please go over it.
Alright, I fixed a few typos (that I made), and it looks good to me now.
Thanks. Funny to me that the French have a common word for this, but the English have never felt the need for it. (I certainly never have.) I’d be more inclined to name the page quadrable cospan, thoughts?
Well, it would be completely pointless to make coquadrable span and quadrable cospan and (co)-quadrability of a category all separate articles. This title gives you all things quadrable!
Anyway, a filter on a poset is a quadrable upper set. In fact, the reason that I wrote this entry was so I could say that.
Of course, what I meant was that I would be inclined to make the title of the page “quadrable cospan” with “quadrability” a redirect, rather than vice versa. I think our usual convention is to name pages after things in mathematics, rather than properties.
I would be inclined to regard that definition of a filter as making simple things difficult, but YMMV. (-: I think it’s also wrong in that it doesn’t require the filter to be nonempty, and even then it only agrees with the usual definition if your poset is upwards-directed, since otherwise not every pair of elements can be completed to a cospan.
I think it's also wrong in that it doesn't require the filter to be nonempty, and even then it only agrees with the usual definition if your poset is upwards-directed, since otherwise not every pair of elements can be completed to a cospan.
True.
If you want to change it to “squarable”, then I don’t mind that either, but “quadrable” is proper English, while “squarable” isn’t.
I don’t really care what it’s called, but what’s improper about “squarable”?
It's not a word! Quadrable is the word meaning squarable!
Exclamation points notwithstanding, I guess I don’t understand what the argument is that “it’s not a word”. I mean, it’s a term that people frequently use, with various clear (albeit context-dependent) agreed-upon meanings… It seems to me there’s all the same kinds of evidence for “squarable” being a word as there is for “quadrable” or even, say, “functor” being words (not that I would consider it to take terribly much for a thing to “be a word”). As far as I’m concerned, “quadrable” and “squarable” are synonyms. But, whatever; I don’t terribly care. I was just curious what the reasoning was.
No, quadrable is in the dictionary!
I was just curious what the reasoning was.
I suppose Harry is just indulging in advanced procrastination of his homework. ;-)
I suppose Harry is just indulging in advanced procrastination of his homework. ;-)
If procrastination were a marketable skill, I probably still wouldn't make money for it because I'd procrastinate until I hit the deadline for filling out the paperwork.
For what it’s worth, “quadrable” sounds much better to my ears than “squarable”. I keep wanting to say “scrabble” or some such other mangling: the “r” in the middle gets slurred when I try to say it. Both would be fantastic scrabble words, of course (you’d have to do something like starting with “able” and extending left).
Yes, they’d be good Scrabble words all right – but the fact they’re both nine letters long is pretty inconvenient. Probably an expert wouldn’t leave -able along a triple word line! :-)
Since when have mathematicians ever been bothered by calling something by a word that isn’t in the dictionary? Some of the best words in mathematics aren’t in the dictionary – if you make up your own word, you can be sure no one has ever used it to mean something else before!
Since when have mathematicians ever been bothered by calling something by a word that isn't in the dictionary? Some of the best words in mathematics aren't in the dictionary -- if you make up your own word, you can be sure no one has ever used it to mean something else before!
Because it's the correct translation of the french word "carrable"! I'm not going to change it, but if you feel compelled to change it, go ahead. Just know that I'll hate you forever for it :'(
=p
hey, I’m just joking around here. I like quadrable better than squarable; squarable sounds to me like a number such that exists. But if I liked squarable better, I wouldn’t hesitate to use it despite its not being in the dictionary. (-:
hey, I'm just joking around here.
What a coincidence, me too! =)
Link: http://www.math.univ-toulouse.fr/~toen/m2.html is invalid. There is no webpage of Bertrand Toen at Toulouse.
Changed to: https://perso.math.univ-toulouse.fr/btoen/files/2015/02/cours2.pdf and name of the course to mach info from Bertrand Toen home page (https://perso.math.univ-toulouse.fr/btoen/videos-lecture-notes-etc/).
Add reference to André Joyal publication Notes on Clans and Tribes that define and uses carrable rather than quadrable.
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