Re: The Wikibook on Category Theory

Re: The Wikibook on Category Theory

[Urs Schreiber]

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.


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Re: The Wikibook on Category Theory

[Björn Gohla]

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




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Re: The Wikibook on Category Theory

[Andrew Stacey]

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.

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Re: The Wikibook on Category Theory

[Andrew Salch]

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
>

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Re: The Wikibook on Category Theory

[Charles Wells]

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


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Re: The Wikibook on Category Theory

[Urs Schreiber]

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


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Re: The Wikibook on Category Theory

[Michael Shulman]

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.
>

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Re: The Wikibook on Category Theory

[Mike Stay]

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


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The Wikibook on Category Theory

[Charles Wells]

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



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