RE: Timelines for category theory: a response to comments

RE: Timelines for category theory: a response to comments

[André Joyal]

Dear Ronnie and George,

The timeline of a field is a time ordered list of the significant  
developments of this field.
Of course, one may disagree on what is significant.
A timeline is inherently cahotic, since many developements are  
inherently unpredictable.
Some developements are influenced by what is happening outside the  
field.
It would be wrong to organise a timeline as if it were a plan for a  
course in category theory.

Of course,  we could have a timeline for topos theory, or for any sub- 
discipline of category theory.

Best,-André

-------- Message d'origine--------
De: Ronnie Brown [mailto:ronnie.profbrown@btinternet.com]
Date: dim. 10/07/2011 13:03
À: categories@mta.ca
Cc: George Janelidze
Objet : categories: Timelines for category theory: a response to  
comments

Dear Colleagues,

Many thanks for your comments, which show how our community sees the
problem. The discussion is obviously not finished yet.

Let us actually try to say what is the MAIN problem with this article.
The main problem is the picture of category theory it draws! Many of you
give courses in category theory at various levels - beautiful courses
showing that category theory provides a new most advanced level of
thinking in mathematics ("thinking categorically!"), and has made major
contributions to the unity of mathematics. So, why don't you compare the
plan of your own course with this article? Surely you do not begin your
course with resolutions of modules and you do not end it with "extended
TQFT", do you?

On the other hand there is clearly a desire to have a good content  and
context for category theory on wikipedia, which is often the first port
of call for students, and those potentially interested, and so there are
calls for an improved Timeline for category theory. To take in the whole
subject in one timeline, with references, would seem an enormous and
controversial task.

We therefore propose that the present article be replaced by  a list of
topics with links to articles on timelines of those topics. And then
each "timeline" should be written by a chosen group of experts. Our
first draft of topics would be:

1. General category theory, including motivation
2. Abelian categories and homological algebra
3. Categories and groupoids in homotopical algebra and algebraic  
topology
4. Topos theory
5. Monoidal, enriched, and higher-dimensional categories
6. Categorical algebra
7. Categorical topology
8. Categorical logic and foundation of mathematics
10. Categories in algebraic geometry
11. Categories in computer science
12. Categories in Physics

There will be intersections of course, but we presume that is fine.

As examples of timelines in other subjects, and their styles, see for
example

http://en.wikipedia.org/wiki/List_of_timelines#Science

particularly those on Physics.

We look forward to reactions to this proposal.

Ronnie Brown

George Janelidze



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

RE: Timelines for category theory: a response to comments

[Michael Barr]

I take it from this list that the developments of the '60s involving
"triple cohomology" and acyclic models is not considered of
importance in the history of category theory.

This comment shows how difficult it is to construct such a timeline that
will satisfy everybody.

Michael

> Our
> first draft of topics would be:
>
> 1. General category theory, including motivation
> 2. Abelian categories and homological algebra
> 3. Categories and groupoids in homotopical algebra and algebraic
> topology
> 4. Topos theory
> 5. Monoidal, enriched, and higher-dimensional categories
> 6. Categorical algebra
> 7. Categorical topology
> 8. Categorical logic and foundation of mathematics
> 10. Categories in algebraic geometry
> 11. Categories in computer science
> 12. Categories in Physics
>
> There will be intersections of course, but we presume that is
> fine.
>
> As examples of timelines in other subjects, and their styles,
> see for
> example
>
> http://en.wikipedia.org/wiki/List_of_timelines#Science
>
> particularly those on Physics.
>
> We look forward to reactions to this proposal.
>
> Ronnie Brown
>
> George Janelidze
>
>


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Timelines for category theory: a response to comments

[Graham White]

I think, judging by comments so far, that there are basically two
goals concealed within "this project". One is to write an outline of
category theory as it seems to us now; the other is to write a history
of category theory, and, specifically, a history of who influenced whom.
Both of these are very worth doing, but the second is much more
difficult.

It's difficult mainly because it entails recovering a consistent history
from people's reminiscences, and these will not be consistent with
each other: they will be inconsistent not just because people's memories
are not accurate, but because everyone has remained active in the field
and they alter their memories according to what they think now. This is
probably especially true of mathematicians, because mathematicians
always rephrase other people's stuff in their own terms: it's how they
come to understand it. (Remember Goethe's remark, "Mathematicians are
like Frenchmen: if you tell them something, they rephrase it in their
own language, and you cannot understand it any more"? Well,
mathematicians do that to each other as well as to non-mathematicians).

The history is hard to do, but also potentially very valuable: it would
show how a revolution in mathematics took place. Hard work, though.

And *not* in the form of a Wiki, because Wikis deal with contradictions
between documents by erasing one document in favour of the other. (I
know, you can always look back in edit history, but it still relegates
one of the testimonies to the sidelines: you might well be in a
situation where you just have more than one testimony, and where it
would not be sensible to prefer one to the other).

Graham

On Tue, Jul 12, 2011 at 06:48:53AM +0930, David Roberts wrote:
> Hi Ronnie,
>
>> ....Our first draft of topics would be:
>>
>> 1. General category theory, including motivation
>> 2. Abelian categories and homological algebra
>> 3. Categories and groupoids in homotopical algebra and algebraic topology
>> 4. Topos theory
>> 5. Monoidal, enriched, and higher-dimensional categories
>> 6. Categorical algebra
>> 7. Categorical topology
>> 8. Categorical logic and foundation of mathematics
>> 10. Categories in algebraic geometry
>> 11. Categories in computer science
>> 12. Categories in Physics
>
>
> a good candidate for what your 12., combined with 11., 8. and a bit of 5.  might
> look like is Baez and Stay's 'Rosetta stone' paper, see:
>
> http://golem.ph.utexas.edu/category/2008/03/physics_topology_logic_and_com.html
>
> Clearly this is only a tiny slice of the category theory cake, and perhaps again
> a biased one, but at least it contains facts, and references.
>
> Best of luck with this project, I look forward to contributing in what small way
> I can.
>
> David
>

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Re: Timelines for category theory: a response to comments

[Jeremy Gibbons]

If I may stick my head over the parapet, I'd like to suggest that you're surely fighting a losing battle here. Wikipedia does not work by having articles written by "chosen groups of experts". Indeed, quite the opposite; some amateur with community spirit and a personal itch to scratch makes a start, others - perhaps more expert - chip in, and gradually the wonder that is Wikipedia blossoms. Or not, as the case may be: perhaps two amateurs with conflicting axes to grind hack away at each other's changes, and nothing productive comes of it; that's the price you pay for crowd-sourcing.

I believe that your only option is to do some of that chipping in yourself. You can obviously see many flaws in the original article that "Fotino" has kindly started; why not set about improving it? Who knows - others may follow your noble example! 

But I recommend not to start by replacing the existing article with a blank slate; that's simply rude. If in doubt, start with the associated discussion page, which doesn't seem to have changed since Oct 2009. See the discussion under "Stub requests"; maybe talk personally with Charles Matthews.

Jeremy

On 10 Jul 2011, at 18:03, Ronnie Brown wrote:

> Dear Colleagues,
> 
> Many thanks for your comments, which show how our community sees the
> problem. The discussion is obviously not finished yet.
> 
> Let us actually try to say what is the MAIN problem with this article.
> The main problem is the picture of category theory it draws! Many of you
> give courses in category theory at various levels - beautiful courses
> showing that category theory provides a new most advanced level of
> thinking in mathematics ("thinking categorically!"), and has made major
> contributions to the unity of mathematics. So, why don't you compare the
> plan of your own course with this article? Surely you do not begin your
> course with resolutions of modules and you do not end it with "extended
> TQFT", do you?
> 
> On the other hand there is clearly a desire to have a good content  and
> context for category theory on wikipedia, which is often the first port
> of call for students, and those potentially interested, and so there are
> calls for an improved Timeline for category theory. To take in the whole
> subject in one timeline, with references, would seem an enormous and
> controversial task.
> 
> We therefore propose that the present article be replaced by  a list of
> topics with links to articles on timelines of those topics. And then
> each "timeline" should be written by a chosen group of experts. Our
> first draft of topics would be:
> 
> 1. General category theory, including motivation
> 2. Abelian categories and homological algebra
> 3. Categories and groupoids in homotopical algebra and algebraic topology
> 4. Topos theory
> 5. Monoidal, enriched, and higher-dimensional categories
> 6. Categorical algebra
> 7. Categorical topology
> 8. Categorical logic and foundation of mathematics
> 10. Categories in algebraic geometry
> 11. Categories in computer science
> 12. Categories in Physics
> 
> There will be intersections of course, but we presume that is fine.
> 
> As examples of timelines in other subjects, and their styles, see for
> example
> 
> http://en.wikipedia.org/wiki/List_of_timelines#Science
> 
> particularly those on Physics.
> 
> We look forward to reactions to this proposal.
> 
> Ronnie Brown
> 
> George Janelidze
> 

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Timelines for category theory: a response to comments

[David Roberts]

Hi Ronnie,

> ....Our first draft of topics would be:
>
> 1. General category theory, including motivation
> 2. Abelian categories and homological algebra
> 3. Categories and groupoids in homotopical algebra and algebraic topology
> 4. Topos theory
> 5. Monoidal, enriched, and higher-dimensional categories
> 6. Categorical algebra
> 7. Categorical topology
> 8. Categorical logic and foundation of mathematics
> 10. Categories in algebraic geometry
> 11. Categories in computer science
> 12. Categories in Physics


a good candidate for what your 12., combined with 11., 8. and a bit of 5.  might
look like is Baez and Stay's 'Rosetta stone' paper, see:

http://golem.ph.utexas.edu/category/2008/03/physics_topology_logic_and_com.html

Clearly this is only a tiny slice of the category theory cake, and perhaps again
a biased one, but at least it contains facts, and references.

Best of luck with this project, I look forward to contributing in what small way
I can.

David


------------------------------
David Roberts

david.roberts@adelaide.edu.au
University of Adelaide



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Timelines for category theory: a response to comments

[Sergei SOLOVIEV]

I think that the list of topics is very good, and the idea seems to me
very reasonnable.

And with all my respect to Eduardo ("No censorship to wikipedia !") I
don't think
that everything should be reduced to mere opinions and freedom of speech
- there is
also the notion of truth. Supposedly, the above mentioned freedom should
help
to find it, at least, in science.

Best regards

Sergei Soloviev

Ronnie Brown wrote:
> Dear Colleagues,
>
> Many thanks for your comments, which show how our community sees the
> problem. The discussion is obviously not finished yet.
>
> Let us actually try to say what is the MAIN problem with this article.
> The main problem is the picture of category theory it draws! Many of you
> give courses in category theory at various levels - beautiful courses
> showing that category theory provides a new most advanced level of
> thinking in mathematics ("thinking categorically!"), and has made major
> contributions to the unity of mathematics. So, why don't you compare the
> plan of your own course with this article? Surely you do not begin your
> course with resolutions of modules and you do not end it with "extended
> TQFT", do you?
>
> On the other hand there is clearly a desire to have a good content  and
> context for category theory on wikipedia, which is often the first port
> of call for students, and those potentially interested, and so there are
> calls for an improved Timeline for category theory. To take in the whole
> subject in one timeline, with references, would seem an enormous and
> controversial task.
>
> We therefore propose that the present article be replaced by  a list of
> topics with links to articles on timelines of those topics. And then
> each "timeline" should be written by a chosen group of experts. Our
> first draft of topics would be:
>
> 1. General category theory, including motivation
> 2. Abelian categories and homological algebra
> 3. Categories and groupoids in homotopical algebra and algebraic topology
> 4. Topos theory
> 5. Monoidal, enriched, and higher-dimensional categories
> 6. Categorical algebra
> 7. Categorical topology
> 8. Categorical logic and foundation of mathematics
> 10. Categories in algebraic geometry
> 11. Categories in computer science
> 12. Categories in Physics
>
> There will be intersections of course, but we presume that is fine.
>
> As examples of timelines in other subjects, and their styles, see for
> example
>
> http://en.wikipedia.org/wiki/List_of_timelines#Science
>
> particularly those on Physics.
>
> We look forward to reactions to this proposal.
>
> Ronnie Brown
>
> George Janelidze


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: Timelines for category theory: a response to comments

[Robert Dawson]

Ronnie Brown wrote:

> We therefore propose that the present article be replaced by a list of
> topics with links to articles on timelines of those topics. And then
> each "timeline" should be written by a chosen group of experts. Our
> first draft of topics would be:

 	Ronnie:

 		No doubt the project you have described is an excellent one, but
"propose that the article be replaced" just isn't how Wikipedia works -
let alone "should be written by a chosen group of experts."

 	This is like suggesting that a school talent show would be better if
instead of having all those random kids singing & dancing they hired
some real professionals.  Or like saying MacDonald's would be a great
restaurant if they ditched the burgers and chips.

 	There's nothing stopping you from putting together the project you
describe; and some parts of it could be accomplished on Wikipedia. But
why?  It could not be exactly what you want, and conversely you don't
seem to think the Wikipedia model is very useful for what you would like
to do.  There are lots of other Internet service providers out there.

 	Cheers,
 		Robert





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Re: Timelines for category theory: a response to comments

[jim stasheff]

On 7/10/11 1:03 PM, Ronnie Brown wrote:
> 1. General category theory, including motivation
Trivial but important suggestion

add

0. Motivation for cat theory

   before anything technical

maybe that can be a compilation of motivationS derived from the other topics


jim



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Timelines for category theory: a response to comments

[Ronnie Brown]

Dear Colleagues,

Many thanks for your comments, which show how our community sees the
problem. The discussion is obviously not finished yet.

Let us actually try to say what is the MAIN problem with this article.
The main problem is the picture of category theory it draws! Many of you
give courses in category theory at various levels - beautiful courses
showing that category theory provides a new most advanced level of
thinking in mathematics ("thinking categorically!"), and has made major
contributions to the unity of mathematics. So, why don't you compare the
plan of your own course with this article? Surely you do not begin your
course with resolutions of modules and you do not end it with "extended
TQFT", do you?

On the other hand there is clearly a desire to have a good content  and
context for category theory on wikipedia, which is often the first port
of call for students, and those potentially interested, and so there are
calls for an improved Timeline for category theory. To take in the whole
subject in one timeline, with references, would seem an enormous and
controversial task.

We therefore propose that the present article be replaced by  a list of
topics with links to articles on timelines of those topics. And then
each "timeline" should be written by a chosen group of experts. Our
first draft of topics would be:

1. General category theory, including motivation
2. Abelian categories and homological algebra
3. Categories and groupoids in homotopical algebra and algebraic topology
4. Topos theory
5. Monoidal, enriched, and higher-dimensional categories
6. Categorical algebra
7. Categorical topology
8. Categorical logic and foundation of mathematics
10. Categories in algebraic geometry
11. Categories in computer science
12. Categories in Physics

There will be intersections of course, but we presume that is fine.

As examples of timelines in other subjects, and their styles, see for
example

http://en.wikipedia.org/wiki/List_of_timelines#Science

particularly those on Physics.

We look forward to reactions to this proposal.

Ronnie Brown

George Janelidze


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]