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I wrote down a definition at pseudofunctor.
I thought that, typically, “pseudo” is reserved for strong 2-functors between strict 2-categories (often for a strong 2-functor from a 1-category into ).
For Grothendieck pseudofunctors were from 1-category into 2-category. Pseudo now just means lax with invertible coherences. I agree with the article. Though, in the case of bicategories, indeed, the Australian school likes also the name "homomorphism of bicategories".
Some people say pseudofunctor also for pseudo-n-functor where n is bigger than the default 2. Now if one wantsd to use number than there is a clash between n-pseudofunctor and pseudo-n-functor, where if we were to follow the tradition on categorification the n in one and the other expression would not agree. n-pseudofunctor would be a pseudo-(n+1)-functor whose domain is n-category.
“homomorphism of bicategories”.
this is Benabou. I think Kelly preferred ’functor’ between bicategories.
I agree with David 4, pseudofunctors are the “default” sort of functor between bicategories; the “pseudo” is only necessary when there’s a danger of confusion. That means maybe it’s used more often when the 2-categories are strict, since it’s in that case that strict 2-functors appear more frequently and might need to be disambiguated from. But I don’t think it’s wrong to use it for weak 2-categories if you want to emphasize its pseudo-ness.
BTW, you wrote the constraint isos in the “oplax” direction, so I changed the final section to align with this. Any reason why you chose that direction?
A guess about Toby’s motivation with an opinion: The oplax direction looks more like distribution over the product and seems more natural coming from an algebraic background, at least to me.
I think that this page is at pseudofunctor (Mike might know, unless the page was moved after he began it) simply because this is the name that means primarily this concept. I would usually follow Kelley and just say ‘functor’, but you have to know the context.
But the special case of a functor to from a -category is an important one; perhaps it should be mentioned explicitly?
Mike asks:
Any reason why you chose that direction?
It was the direction that I saw suggested in the query box on that page. I didn’t notice that your comment, identifying one direction as ‘lax’ and noting its connection to Grothendieck fibrations, was opposite to Tim’s comment. I actually meant to follow yours (since you gave a reason for yours), but I don’t suppose that it really matters. Thanks for the fix on the names.
ETA: I opened the page to fix a typo and ended up changing to the lax convention after all. BTW, in the diagrams, you can still argue about the directions of the associators and unitors if you like (not to mention the order of composition), but at least that doesn’t go into the structure in the definition.
What is ETA ?
I thought it meant estimated time of arrival! :-)
It also stands for Euskadi Ta Askatasuna which is not to be messed with, but I suspect Edited to ADD.
That is he meant more traditional, P.S. post scriptum ?
I wrote a history section for the French history of the notion until 1967. For later somebody from Australia (David ?) should write, I am not sure about how the things went.
I think that making a separate acronym language for internet users is ugly from many respects and I have no wish to become a user of yet another unnecessary jargon. Webspace is wide so why not write full words.
Well, at least we have a handy-dandy site to bookmark. I didn’t know ETA (with this meaning) either, and Zoran has a point. OTOH, if you’re trying to write a comment on MO and are confined to 600 characters, such things occasionally come in handy.
I can always write two comments in MO :) On the other hand, yes Toby, thanks for the bookmark :)
z0r4n wh4t R U t41king ab0uT?!? U R behind the times!!!!!! (-:O
Todd, I presume your simultaneous use of another Internet abbreviation was intentional? (-: I think some of them come in handy; it’s okay to be a bit lazy even when you aren’t under a draconian character limit. But that meaning of ETA seems pretty superfluous to me; I thought people usually just wrote “Edit:” which is about the same length.
Yes, I was ribbing Zoran a little (even though I had already written OT before it became intention (-: ).
IMO (ha!), excessive initializing is a move in a direction away from good “netiquette”. Really, I am irritated on an almost daily basis by the curtness and lack of human feeling in internet messages – not to mention by the steady degradation of the English language, which is a beautiful instrument. “Anyhoo”…
0T<- that is 0 not O!
Usage of specialized artifical language by specialized groups is always making it impenetrable by the exterior world, unfriendly to people who hang there just occasionally or who have intention to keep simulatenously in many communities and hence do not have time to stabilize on too specific local conventions. Imagine now English internet abbreviations, Russian internet abbreviations, French internet abbreviations, then radio abbreviations (I was using Morse some 2 decades ago and still like it; they have their own abbreviations), the journal abbreviations etc. I spend much internet time in Russian and Croatian internet community for example. But I think that in general both Russian and American societies use too many abbreviations anyway and I was often obstructed in understanding for that reason. Yes, here Edit was understandable from the very first usage and nobody needed to explain. 5-6 major abbreviations in each particular segment of human activity is about enough apart from 2-3 major ones. If one has 20-30 activities this amounts to more than enough. Do you know what is JIES for example ? This is in another (now dormant) activity of mine a must.
IMHO, if one needs to go to special dictionaries of abbreviations this is not a solution to the problem but an indicator (that it became/of) a problem.
Tim: on the internet, among people speaking Russian, 4 is very often the letter transliterating cyrillic ч (ch), cf. http://translit.ru.
Zoran, I no longer recall what you think about the problem of evil (non-kosher, privatio boni, however you wish to put it), but my guess would be that you don’t like this either. (There is an awful lot of current discussion about this at the categories list, and it has the feeling of mostly being a generation gap thing. I’m sort of with Toby: it’s so obviously tongue-in-cheek, I think it’s harmless. Better than “fascist”!)
No, I don’t know what JIES stands for.
I recall arriving at the Campus Beaulieu in Rennes, going to give a seminar and to talk with Daniel Conduché. There was a panel of acronyms, all in big letters, but not a single explanation! I have seen the same thing at numerous other campuses in various parts of the world, and it seems to me that as Zoran implies they block understanding and are inefficient. I wondered how someone who had to deliver something to the Department of Mathematics at the Université de Rennes would find the maths building from the information on that panel. (There was no ’porters’ lodge’ as one finds in someplaces.) So it is not just on the net that these annoyances occur.
Text messages on phones are annoying but perhaps more excusable due to space limitations, but they lead to bad spelling.
I sometimes use nPOV but that is more for fun than being necessary. :-)
The use of the query box on pseudofunctor could be taken as an example. I tried to suggest that the direction concerned the presentation of the pseudofunctor not it itself. That comment is still there and the discussion is I hope useful. The fact that it is discussion rather than main text is good here as that point is one that might help someone but is not central to the understanding of pseudofunctors.
20 zskoda
Usage of specialized artifical language by specialized groups is always making it impenetrable by the exterior world, unfriendly to people who hang there just occasionally …
Yeah! Like in most of Mathematics. Why do mathematician insist on using the opaque word “abelian” when there is the more transparent word “commutative”.
Ah! Firstly it is to honour Abel of course, but also ’commutative’ is overused. A commutative ring is not an Abelian object in the category of rings as that would have to have zero multiplication. Our problem is there are lots more concepts than there are words to fit them!
I understand the problem of the outsider as I was involved in quite a few cross disciplinary research groups. Mathematicians are bad but nowhere like as bad as biochemists, neurophysicists, etc. and do not mention people who work in applied linguistics!
I am not convinced that ‘commutative’ is better as it is not understandable by real outsiders either (or by undergraduates at least to start with).
About evil ? Well before we had a discussion in which I had some other term I do not recall, but anyway in general it is not the same as invariant under equivalence, the way John Baez defines it. Most of the time one means invariant under equivalence for a property. But often one looks at creating a version of a construction involving possibly several objects not in a single category, rather than a property. Then the definition of the wanted thing is not clear and only if one defines the optimal category of things expressing it it will reduce to invariant under equivalence. Thus if one means only invariant under equivalence I prefer that, but if one means some construction involving several things and the output of a construction is not merely an object of some clear to state category than we need to talk about maximnal weakness or whatever variant of more vague and general group of notions is...
Really, I am irritated on an almost daily basis by the curtness and lack of human feeling in internet messages – not to mention by the steady degradation of the English language, which is a beautiful instrument.
+1. (ha!)
I wrote ‘ETA’ because I’d recently been reading a different forum, on which it was common. Zoran is right: better just to say ‘Edit:’. However, I really don’t mind it when people use acronyms on the web, because I can just look them up.
There is a difference in my mind, a sort of generation gap in miniature, between the abbreviations that were common in email and Usenet in the 1990s and newer abbreviations from the forums and blogs today. So ‘IMHO’ feels like part of my native tongue, while ‘ETA’ is not.
One good feature that I’ve learnt from forum culture is using
@ <name>
to indicate to whom one is replying. Much better than
On <date> in <messageID>, <name> wrote:
Don’t you think so? (^_^)
PPS: We’re not losing any actual discussion of pseudofunctors here, are we?
PS: horizontal emoticons
Ah, I had always thought that this was your private invention and way of using emoticons!
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