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/ ]
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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/ ]
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/ ]
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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/ ]
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.h... 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/ ]
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.h...
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
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
From: "Eduardo J. Dubuc" <edubuc@dm.uba.ar> Date: Sat, 09 Jul 2011 16:48:59 -0300
Before the net and wikipedia the only people which had the possibility of a large audience where "the authorities", prestigious people on their field. We all were bounded by their view of things.
Now everybody interested have the same chance to expose his (or hers) own version of a subject.
Reminiscent of this paragraph. "http://en.wikipedia.org/wiki/Democratization#Knowledge" From: Graham White <graham@eecs.qmul.ac.uk> Date: Tue, 12 Jul 2011 17:13:34 +0100
... two goals concealed within "this project". One is to write an outline of category theory as it seems to us now; ...
Reminiscent of this article. "http://en.wikipedia.org/wiki/Outline_of_category_theory" Best regards to everyone, ... Peter E. -- Telephone 1 360 450 2132. bcc: peasthope at shaw.ca Shop pages http://carnot.yi.org/ accessible as long as the old drives survive. Personal pages http://members.shaw.ca/peasthope/ . [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Can we do history of category theory without considering history leading to category theory? Is history an attachment of subhistories, or are there paths that can be followed, and how do we teach these things to young researchers? What I say is I like the '... and foundations of mathematics'. I always wondered if the term 'categorical this-and-that' every once in a while should be considered with its counterpart 'this-and-thatical category theory'. It's also about meta and object languages, I believe. And sometimes categorists 'internalize', so that the roles of meta and object ar blurred. Isn't a topos basically a 'logical category', where 'categorical logic' is something else? 'Topological category' is not the same as 'categorical topology', and so on. Also, 'categories in computer science' is too general. Still, most of categories, used in recognized areas in computer science, relate to logic in one way or the other, and to logic in a broad sense. Sometimes we also say computer science has given many interesting problems for category theory. I don't think this is really true in such a phrasing. What has happened is that computer scientist in their work to formalize computable logic and computability has been forced to go back to foundations of mathematics in order to understand what is really going on. Computer scientists, however, usually don't bother to formalize something they already 'understand' (type theory is a good example), where a mathematicians refuses to understand before it's formalized (that's why there isn't any mathematical type theory). Yes, we can. We can do history of category theory without considering history leading to category theory. But why should we? And how does it help to bring out all flavours of things we are still working on? Will this history writing provide me with those utensils I need for things I need to do. Or do I have to go elsewhere to look for it? History writing is also a bit dangerous as it almost says this is now the state-of-the-art, and if you don't play your etudes properly you are not allowed to play structure and provide interpration. Talent is thereby often surpressed, and mostly by teachers who really never understood counterpoint anyway. So what I really say is I like the '... and foundations of mathematics'. Keeping meta and object apart, and category theory taught me how to do that, is important for logic and foundations, as we know e.g. from Gödel numbering and creating sentences about it. To which logic these sentences belong, nobody ever told me, so please do. Best regards, Patrik On Tue, 12 Jul 2011, Graham White wrote:
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
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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/ ]
participants (11)
-
André Joyal -
David Roberts -
Graham White -
Jeremy Gibbons -
jim stasheff -
Michael Barr -
Patrik Eklund -
peasthope＠shaw.ca -
Robert Dawson -
Ronnie Brown -
Sergei SOLOVIEV