The Category Theory book on Wikibooks<http://en.wikibooks.org/wiki/Category_Theory>has been languishing for three years, except for some good work done by Physis <http://en.wikibooks.org/wiki/User:Physis>. I have spent the last two days reorganizing it and cleaning it up. I have broken the book into pages and introduced some stubs. I have rewritten the Introduction and most of the chapter on Categories. The chapter on Natural Transformations covers the topic but I recommend it be rewritten in a more labeled style with bulleted lists, subsections, etc (like the Categories chapter) The other chapters need to be completely rewritten to fix the TeX, get rid of the page references (to someone's lecture notes, presumably), and so on. This is a good project for retired category theorists. Younger mathematicians get no academic rewards at all for contributing to Wikis. Note: If you are interested in something special, just write it up! For example you could write up typed lambda-calculus as an example, or a section on sheaves, or an introduction to 2-categories. If you need to refer to something not yet written, just add a stub. *Wikibooks do not have to be done in order. * -- professional website: http://www.cwru.edu/artsci/math/wells/home.html blog: http://sixwingedseraph.wordpress.com/ abstract math website: http://www.abstractmath.org/MM//MMIntro.htm astounding math stories: http://www.abstractmath.org/MM//MMAstoundingMath.htm personal website: http://www.abstractmath.org/Personal/index.html sixwingedseraph.facebook.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
There's a lot of content at nLab, the companion wiki to the n-category cafe. http://ncatlab.org/nlab/show/HomePage On Thu, Aug 13, 2009 at 9:14 AM, Charles Wells<charles@abstractmath.org> wrote:
The Category Theory book on Wikibooks<http://en.wikibooks.org/wiki/Category_Theory>has been languishing for three years, except for some good work done by Physis <http://en.wikibooks.org/wiki/User:Physis>. I have spent the last two days reorganizing it and cleaning it up. I have broken the book into pages and introduced some stubs. I have rewritten the Introduction and most of the chapter on Categories. The chapter on Natural Transformations covers the topic but I recommend it be rewritten in a more labeled style with bulleted lists, subsections, etc (like the Categories chapter) The other chapters need to be completely rewritten to fix the TeX, get rid of the page references (to someone's lecture notes, presumably), and so on.
This is a good project for retired category theorists. Younger mathematicians get no academic rewards at all for contributing to Wikis.
Note: If you are interested in something special, just write it up! For example you could write up typed lambda-calculus as an example, or a section on sheaves, or an introduction to 2-categories. If you need to refer to something not yet written, just add a stub. *Wikibooks do not have to be done in order. *
-- professional website: http://www.cwru.edu/artsci/math/wells/home.html blog: http://sixwingedseraph.wordpress.com/ abstract math website: http://www.abstractmath.org/MM//MMIntro.htm astounding math stories: http://www.abstractmath.org/MM//MMAstoundingMath.htm personal website: http://www.abstractmath.org/Personal/index.html sixwingedseraph.facebook.com
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
On Thu, Aug 13, 2009 at 6:14 PM, Charles Wells<charles@abstractmath.org> wrote:
The Category Theory book on Wikibooks<http://en.wikibooks.org/wiki/Category_Theory>has been languishing for three years, except for some good work done by Physis <http://en.wikibooks.org/wiki/User:Physis>. I have spent the last two days reorganizing it and cleaning it up.
It might be worthwhile merging this effort with that at the nLab wiki. It seems to me that this has by now entries on most or all of the planned entries at the wikibook -- and more. Maybe one should transfer material as needed. To get an impression for the entries that do and those that do not yet exist on the nLab see the link lists at [[category theory]] http://ncatlab.org/nlab/show/category+theory [[Categories and Sheaves]] http://ncatlab.org/nlab/show/Categories+and+Sheaves [[Sheaves in Geometry and Logic]] http://ncatlab.org/nlab/show/Sheaves+in+Geometry+and+Logic There is more, not indexed yet. On the other hand, of course all this is incomplete and still in the making, too. Please feel free and feel encouraged to add to the nLab. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
I love the nLab too, but I'm not sure that "merging" is the right word; probably the two are serving slightly different purposes. The overall nLab is not really organized like a textbook or designed to be read linearly; writing a textbook requires additional thought. But there is certainly no reason why the two can't share material and link to each other as appropriate. And/or one could choose to write a textbook as a section of the nLab rather than on Wikibooks (if, for instance, one preferred its offerings in the way of mathematical typesetting). Mike On Fri, Aug 14, 2009 at 6:04 PM, Urs Schreiber<urs.schreiber@googlemail.com> wrote:
On Thu, Aug 13, 2009 at 6:14 PM, Charles Wells<charles@abstractmath.org> wrote:
The Category Theory book on Wikibooks<http://en.wikibooks.org/wiki/Category_Theory>has been languishing for three years, except for some good work done by Physis <http://en.wikibooks.org/wiki/User:Physis>. I have spent the last two days reorganizing it and cleaning it up.
It might be worthwhile merging this effort with that at the nLab wiki. It seems to me that this has by now entries on most or all of the planned entries at the wikibook -- and more. Maybe one should transfer material as needed.
To get an impression for the entries that do and those that do not yet exist on the nLab see the link lists at
[[category theory]] http://ncatlab.org/nlab/show/category+theory
[[Categories and Sheaves]] http://ncatlab.org/nlab/show/Categories+and+Sheaves
[[Sheaves in Geometry and Logic]] http://ncatlab.org/nlab/show/Sheaves+in+Geometry+and+Logic
There is more, not indexed yet. On the other hand, of course all this is incomplete and still in the making, too.
Please feel free and feel encouraged to add to the nLab.
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
On 8/18/09, Michael Shulman <shulman@math.uchicago.edu> wrote:
I love the nLab too, but I'm not sure that "merging" is the right word; probably the two are serving slightly different purposes. The overall nLab is not really organized like a textbook or designed to be read linearly; writing a textbook requires additional thought. But there is certainly no reason why the two can't share material and link to each other as appropriate.
I agree. Maybe "merging the effort" wasn't a good choice of words, but when I saw the wikibook I had the strong impression that there were similar intentions here to a large piece of the nLab and I thought it should be useful and easy to transfer content and join forces where reasonable and desirable.
And/or one could choose to write a textbook as a section of the nLab rather than on Wikibooks (if, for instance, one preferred its offerings in the way of mathematical typesetting).
Yes, that sounds like an interesting idea. Another advantage might be a greater and easier supply of cross-hyperlinks, either way. In any case, there are many category-theoretic entries (and not just those) on the nLab -- existing ones and not-yet existsing ones -- where I would find more textbook-style material highly desireable. Best, Urs [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
I like the idea of n-labs and wikibooks sharing material. They really do serve different functions, but sharing could make both of them better. A textbook needs to give the basic ideas of category theory in a linear fashion with some proofs spelled out and lots of exercises. The idea is that students could read the introduction and find out which chapters they need to to learn the category theory appropriate to their interests. The chapters should be clearly organized in a tree so you can see what each chapter has as prerequisites. n-labs material on category theory needn't be and shouldn't be organized that way. It is a *lab. *Still, some of the entries in n-labs could be more complete and better organized, and material in the wikibook could provide some of that. And certainly lots of stuff in n-labs could be moved over to a wikibook and, er, textbookized. I don't intend to do a lot of work on the wikibook. I have co-authored two books in categories already. I was hoping to get it organized so people would have a place to write about useful topics, but the response has not been great. One thing that bothers me about wikidom is that there is a wikibook on category theory and also a wikiversity "learning project". The latter is mostly stubs. I am not entirely convinced they should be separate. If they have to be separate, there could be lots of sharing back and forth between those two as well. Another thing that bothers me is that the advice on wikibooks says don't include lots of links. For one thing, wikibooks has a system that can generate a PDF file of a book and if you print it out you can't hit the links. These days when I write wikipedia entries, abstractmath pages and blogs I include lots of links. It goes against the grain, for example, to mention homology groups in an example on functors without linking to the wikipedia article on homology. In five years we will all have decent electronic text readers and that won't be a problem except for old fogies. (I was born in 1937 so I can diss old fogies if I want to.) I have not included links in the little I have written in the wikibook on category theory, but I may change my mind. Charles Wells On Tue, Aug 18, 2009 at 3:42 PM, Urs Schreiber <urs.schreiber@googlemail.com
wrote:
On 8/18/09, Michael Shulman <shulman@math.uchicago.edu> wrote:
I love the nLab too, but I'm not sure that "merging" is the right word; probably the two are serving slightly different purposes. The overall nLab is not really organized like a textbook or designed to be read linearly; writing a textbook requires additional thought. But there is certainly no reason why the two can't share material and link to each other as appropriate.
I agree. Maybe "merging the effort" wasn't a good choice of words, but when I saw the wikibook I had the strong impression that there were similar intentions here to a large piece of the nLab and I thought it should be useful and easy to transfer content and join forces where reasonable and desirable.
And/or one could choose to write a textbook as a section of the nLab rather than on Wikibooks (if, for instance, one preferred its offerings in the way of mathematical typesetting).
Yes, that sounds like an interesting idea. Another advantage might be a greater and easier supply of cross-hyperlinks, either way.
In any case, there are many category-theoretic entries (and not just those) on the nLab -- existing ones and not-yet existsing ones -- where I would find more textbook-style material highly desireable.
Best, Urs
-- professional website: http://www.cwru.edu/artsci/math/wells/home.html blog: http://sixwingedseraph.wordpress.com/ abstract math website: http://www.abstractmath.org/MM//MMIntro.htm astounding math stories: http://www.abstractmath.org/MM//MMAstoundingMath.htm personal website: http://www.abstractmath.org/Personal/index.html sixwingedseraph.facebook.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
I have found nLab very helpful as well, for when I need to look up a definition of some higher-categorical construction and I don't have a book or paper on hand to refer to. I have thought many times, though, that it would be great if there were some Web-accessible database of categories which are commonly encountered in mathematics, and their properties; I often find that I need to know if certain kinds of limits, or colimits, or injective envelopes, etc. etc. etc. exist in a particular category, and having some central database to look at (which would hopefully tell me what I need to know as well as cite whatever paper the result was proved in) would be a lot quicker than having to either search the literature for such a result or try to re-prove the result myself. Does anyone know if there have been any attempts to compile such a database? Thanks, Andrew S. On Tue, 18 Aug 2009, Michael Shulman wrote:
I love the nLab too, but I'm not sure that "merging" is the right word; probably the two are serving slightly different purposes. The overall nLab is not really organized like a textbook or designed to be read linearly; writing a textbook requires additional thought. But there is certainly no reason why the two can't share material and link to each other as appropriate. And/or one could choose to write a textbook as a section of the nLab rather than on Wikibooks (if, for instance, one preferred its offerings in the way of mathematical typesetting).
Mike
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Interesting idea. I've no idea if it's ever been thought of, but I for one would be interested in figuring out if this could be implemented in the n-lab. How many categories do think would actually go into such a database? Would it actually need to be a database, or would a hyperlinked table be sufficient? Andrew On Wed, Aug 19, 2009 at 12:42:46PM -0400, Andrew Salch wrote:
I have found nLab very helpful as well, for when I need to look up a definition of some higher-categorical construction and I don't have a book or paper on hand to refer to. I have thought many times, though, that it would be great if there were some Web-accessible database of categories which are commonly encountered in mathematics, and their properties; I often find that I need to know if certain kinds of limits, or colimits, or injective envelopes, etc. etc. etc. exist in a particular category, and having some central database to look at (which would hopefully tell me what I need to know as well as cite whatever paper the result was proved in) would be a lot quicker than having to either search the literature for such a result or try to re-prove the result myself. Does anyone know if there have been any attempts to compile such a database?
Thanks, Andrew S.
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Andrew Salch wrote: I often find that I need to know if certain kinds of limits, or colimits,
or injective envelopes, etc. etc. etc. exist in a particular category, and having some central database to look at (which would hopefully tell me what I need to know as well as cite whatever paper the result was proved in) would be a lot quicker than having to either search the literature for such a result or try to re-prove the result myself. Does anyone know if there have been any attempts to compile such a database?
I don't know of any such attempts. I've always wanted such a database! An obvious place to create it is on the nLab. I just started one: http://ncatlab.org/nlab/show/database+of+categories but it will only become interesting after a while. If everyone here contributes an entry or two today, it will be interesting by tomorrow! Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
On Thursday August 20 2009, John Baez wrote:
Andrew Salch wrote:
I often find that I need to know if certain kinds of limits, or colimits,
or injective envelopes, etc. etc. etc. exist in a particular category, and having some central database to look at (which would hopefully tell me what I need to know as well as cite whatever paper the result was proved in) would be a lot quicker than having to either search the literature for such a result or try to re-prove the result myself. Does anyone know if there have been any attempts to compile such a database?
I don't know of any such attempts. I've always wanted such a database! An obvious place to create it is on the nLab. I just started one:
http://ncatlab.org/nlab/show/database+of+categories
but it will only become interesting after a while.
If everyone here contributes an entry or two today, it will be interesting by tomorrow! [...]
well, ultimately it would be interesting to have a categorical analogue to «counterexamples in topology». -- regards, björn [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (8)
-
Andrew Salch -
Andrew Stacey -
Björn Gohla -
Charles Wells -
John Baez -
Michael Shulman -
Mike Stay -
Urs Schreiber