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A note on naming pages: generally (with few exceptions) the titles of pages are nouns or noun phrases, singular in number, and in lower case except when someone’s name is involved. Thus, Hausdorff space. As Urs has noted, some categories have such widely accepted abbreviations, and are so intrinsically interesting, that it makes sense to have pages dedicated to them. For example, Set, Top, Ab, Cat.
I am guessing that a lot of the abbreviated names of categories that Stephen listed are the abbreviations used by the authors of The Joy of Cats. Which is a great book, but many of the abbreviations and terminology may be peculiar to the authors. For example, I have not seen or anywhere else.
Here are some assorted quick reactions. Most of the pages are stubs and refer to material developed elsewhere on the nLab, and I don’t particularly want these abbreviations around, since they could be taken as a semi-official endorsement of them by the nLab collective. In some cases I would just as soon delete them (sorry) if they refer to material developed elsewhere on the Lab, and rename them properly and develop them further in cases where the material is new.
I personally feel that , , , , , , , , , , could be deleted without harm. Incidentally, the term “bicompact space” is, I believe, rather antique: it’s what we nowadays call “compact”, if I’m not mistaken. (Confusingly, what was once called “compact” as opposed to “bicompact” is what we nowadays call “countably compact”. :-( )
I didn’t know what a bitopological space was until I looked it up just now. I can’t really attest to its importance. Offhand it strikes me as a somewhat marginal notion, but maybe Toby knows better. If it stays, it should be renamed bitopological space.
I’ll note that care must be taken around ”bornological space” because this means different things to different communities.
The material on automata (), behaviors (), and complete partial orders () deserve to be expanded on in my opinion, but again under different titles.
I agree with Todd, mostly. I think it could be helpful to have CAT either exist on its own or be a redirect to somewhere, since a number of people (myself included) write CAT for the “very large” category of large categories and someone might come here looking for an explanation of what it means. I would suggest that Alg(T) and also T-Alg be redirected to Eilenberg-Moore category, since those are also common enough (and almost universally used with T denoting the monad) that someone might be looking for an explanation of them.
Complete partial orders are, I believe, almost universally called “cpo”s by the people who work with them. And I actually prefer to call them that, since to a category theorist they are not really “complete” at all! But perhaps the page about them should be called cpo, with a remark that the category of such is often called CPO.
I don’t see any harm in keeping bitopological space around; it’s a genuine mathematical concept that some people are interested in, even if we don’t know what for right now.
The other names of categories, I think, aren’t really universal enough to be worthy of inclusion on the nLab, and might create confusion.
Also, another remark about adding references – it’s not really helpful to simply add “see also [[page]]” at the bottom of an existing page, without any explanation of why one might want to see also that page or what its relation is to the current page. It’s good to add references from existing pages to new ones, but you should read the existing page first, make sure that a reference is appropriate, and find a good location on the page to add the reference and also explain it (in complete sentences).
For instance, the references you added to quasicategory were inappropriate, since our usage of quasicategory is totally different from the (fairly archaic) one used in Joy of Cats, which I think you would have seen if you’d read the page quasicategory. (It did, however, suggest to me that other people might have a similar confusion, so I added a remark to that page about the older usage.) As another example, the page partial order already has a section called “Kinds of posets,” so a link to a page about CPOs (being a kind of poset) should go there. The sections called “References” are generally used for links to published papers, preprints, blog posts, other web sites, or other resources outside the nLab.
Hi Stephen,
Don’t sweat it. I think we’re still figuring out what to do. I like the idea of having new pages on automata, behaviors, and cpo’s, and Mike had some constructive suggestions too.
As I said to you privately, we always welcome new input, so if you have something to say on any of the above topics, that would be great! Putting in precise definitions would be wonderful. At the same time, we encourage you to look around the nLab to see how things work, and listen in on discussions at the nForum to get a sense of what’s going on. You might want to visit the Home Page, and in the floating table of contents to the right you see at that page, you will see pages under Community (such as How To, FAQ, etc.) that are worth a visit.
As it happens, we’re having a little party here at my home, so I won’t be able to do anything for the next few hours, unless I sneak away. But I don’t particularly expect you do do anything about the pages you created.
I agree with some of the sentiments expressed so far:
1) it’s great having you on board, Stephen!
2) It’s almost always better to have pages with uncapitalized noun phrases as titles rather than abbreviations. So, instead of adding pages called , , , , , , , , , and , it would be better to create pages with named concepts, or add information to existing pages.
(By the way: “BooSpa” sounds like some business where they tell you ghost stories in a hot tub. I can easily imagine such a thing thriving here in Southern California before the economic crisis. After all, we have a place called The Gourmet Detective in downtown Riverside.)
3) On the other hand, I think CAT and cpo deserve a page, even if the first one is just a quick note that CAT is used as a term for the very large category of large categories.
(Also by the way: we already know how to categorify the concept of partial order, so we can talk about a 2po, a 3po and so on… so when the theory of ’completeness’ is understood, we can define the concept of a c-3po.)
(People who don’t like that picture of a centipede that I put on the Lab as a joke should realize how restrained I’m actually being!)
4) I think it’s better to take the initiative and make changes yourself rather than waiting for someone else to do it.
Yes yes. Welcome Stephen :)
In general, I would follow these steps when adding new material about a given category of objects.
[[!redirects Aut]]) to automaton, so that you can link to that page directly as Aut. At this point, you may find that Aut already existed for some other purpose, so come to the Forum if necessary to figure out what to do.In the past, we sometimes jumped to step 3 in cases where it was obvious that we would reach that step, but I think that the wiki is big enough now that we don’t want to do that.
Also, if you’re going through a book like The Joy of Cats, you should probably really start with step 0:
By the way, I think that it perfectly OK to link to your unofficial table of categories from your personal page on the Lab. To demonstrate how acceptable this is, I have restored the link.
I’m not really happy about Aut redirecting to automaton because “Aut” is also more commonly used to refer to an automorphism group. I would probably add to Toby’s step 3 an additional qualifier like “…and if the notation Aut for the category of automata is, or should be, standard in the literature.”
Step 2 is supposed to help with this, since you see if Aut if redirects somewhere else. Of course a literature search is more certain. But a likely confusion is that ‘’ may well be standard in the literature of automata and yet still have another meaning in another field!
I would like to add to step 2 that you check that any extant links to Aut really want to go to automaton. But unfortunately, we cannot check that sort of thing automatically, at least not until step 3.
Incidentally, the term “bicompact space” is, I believe, rather antique: it’s what we nowadays call “compact”, if I’m not mistaken. (Confusingly, what was once called “compact” as opposed to “bicompact” is what we nowadays call “countably compact”. :-( )
No, they mean a bitopological space whose topologies are both compact (and Hausdorff, in their book). I don’t think that they use any particularly old terminology; they just make up ad hoc names for categories. Perfectly reasonable names (what else would one call the category of automata but ?), but made up for the purpose at hand without any regard for clashes.
While The Joy of Cats seems to be using it in a new way, Mike is right: bicompact space is also a antique term name for ’compact space’. So yeah, no regard for clashes.
OK, Stephen’s pages, following the order of his original list, have now become these pages:
So in short, with the exception of CAT, they have all either become pages about the objects of the category (with the category itself also being discussed there) or they have become ‘history’ pages (our way of deleting a page without deleting its edit history) which link to pages about the objects that already existed.
You should find that, by following the links in Stephen’s original post, that each link takes you directly to an appropriate page. (Nothing should link to the history pages, but they are there for anybody who wants to look at the edit history of the Lab.)
While The Joy of Cats seems to be using it in a new way, Mike is right: bicompact space is also a antique term name for ’compact space’. So yeah, no regard for clashes.
But Joy of Cats is not using this term in a new way! The antique use of ‘bicompact’ is quite antique and, surely, indefensible in a modern book. On the other hand, bitopological spaces are an important field in mathematics, even if I no longer remember clearly what they’re good for, and bitopologists (or whatever you’d call such mathematicians) naturally use the term ‘bicompact space’; Joy of Cats didn’t make it up.
They had no regard for clashes when defining abbreviated names for categories, not when defining terminology for the objects.
what else would one call the category of automata but ?
I wouldn’t call it that, for the reason I mentioned above. For instance, it would lead to writing for the set of automaton-maps from to , which is close to clashing with the standard notation for automorphisms of an object in any category. If you decorate the latter with the category in question, then you would have for the automorphisms of an automaton , which is cute (-: but confusing and quite avoidable; the category could be called or or any number of other things.
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