As evident from the subject, this personal answer to Toby Bartels is intended to have general incumbency. Dear Toby, thanks for this msage, i will try to explain: Toby Bartels wrote:
Eduardo J. Dubuc wrote at first:
Dear Toby, your choice of example is very unfortunate. Mac Lane wrote that category theory was invented to define functor, and that functor was invented to define "natural" transformation.
Yes, I know; that was quite deliberate.
Well, I said "unfortunate" for those that are in favor of introducing the name "evil" (or any other name) as a definition of "not invariant under equivalence". You see, this is because to introduce a name the property has to be important enough and of frequent use. To sustain your case you should have given examples of properties (or concepts) which not being very important and of frequent use, have nevertheless an universally accepted proper name.
but beyond that I have no idea what upsets you, and I'm not going to worry about it any more.
I appreciate that you had worried at some point, and I am glad you do not worry any more. I try to explain why I sounded upset with you in my last mail because it has a general interest concerning the question of whether we are a subculture or part of the mainstream of mathematics. Recall that this was my only mail that concerns you in particular, and that it was in response to a mail of you, and that it was that mail that I felt upsetting. I quote from it:
Shall we stop saying "natural" and say "invariant under composition"? Or is that term allowed under the grandfather clause,
"the grandfather clause" is not something nice to qualify my sayings.
As a proud citizen of the Ghetto of Category Land,
sounds ironic and upsetting, showing that you were very upset that i consider certain characteristics of our group proper of a ghetto, in the sense of isolation from the world of real mathematics. Well, I do think that one of these characteristics is the introduction of names and terminology in an unjustified way. Andre Joyal call it "a subculture" (well, he just said there is a danger to become a subculture) which if you think a little, sounds better than "ghetto", but it is as negatively strong or even worst. I apologize to you for using that term that you had felt insulting (and I imagine some others in the list may have felt so) Your msage had an overall upsetting style, and I reacted accordingly. All the best, no hard feelings from my part. e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Dear all, I'd just like to point out that a quick google search of "category theory evil" gives the correct definition, from the nLab page. As long as articles are referenced properly, this is a non-issue. Moreover, frequently people define things in papers which remain unused outside that one article - as long as everything is clear, there is no problem here. With regards the original problem, that evil is a poor choice, I personally see little point in changing a word no one would be offended by. Ruadhaí On 24 September 2010 16:44, Eduardo J. Dubuc <edubuc@dm.uba.ar> wrote:
As evident from the subject, this personal answer to Toby Bartels is intended to have general incumbency.
Dear Toby, thanks for this msage, i will try to explain:
Eduardo J. Dubuc wrote at first:
Dear Toby, your choice of example is very unfortunate. Mac Lane wrote
Toby Bartels wrote: that category theory was invented to define functor, and that functor was invented to define "natural" transformation.
Yes, I know; that was quite deliberate.
Well, I said "unfortunate" for those that are in favor of introducing the name "evil" (or any other name) as a definition of "not invariant under equivalence". You see, this is because to introduce a name the property has to be important enough and of frequent use. To sustain your case you should have given examples of properties (or concepts) which not being very important and of frequent use, have nevertheless an universally accepted proper name.
but beyond that I have no idea what upsets you, and I'm not going to worry about it any more.
I appreciate that you had worried at some point, and I am glad you do not worry any more.
I try to explain why I sounded upset with you in my last mail because it has a general interest concerning the question of whether we are a subculture or part of the mainstream of mathematics.
Recall that this was my only mail that concerns you in particular, and that it was in response to a mail of you, and that it was that mail that I felt upsetting.
I quote from it:
Shall we stop saying "natural" and say "invariant under composition"? Or is that term allowed under the grandfather clause,
"the grandfather clause" is not something nice to qualify my sayings.
As a proud citizen of the Ghetto of Category Land,
sounds ironic and upsetting, showing that you were very upset that i consider certain characteristics of our group proper of a ghetto, in the sense of isolation from the world of real mathematics. Well, I do think that one of these characteristics is the introduction of names and terminology in an unjustified way. Andre Joyal call it "a subculture" (well, he just said there is a danger to become a subculture) which if you think a little, sounds better than "ghetto", but it is as negatively strong or even worst.
I apologize to you for using that term that you had felt insulting (and I imagine some others in the list may have felt so)
Your msage had an overall upsetting style, and I reacted accordingly.
All the best, no hard feelings from my part. e.d.
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Dear All, I am displeased with the idea that terminology is purely conventional and that everything is acceptable. The "evil" terminology is promoted by a small group of peoples active in the nLab. It does not reflect a commun usage in the mathematical community. Best, André -------- Message d'origine-------- De: Ruadhai [mailto:ruadhai@gmail.com] Date: ven. 24/09/2010 20:38 À: Eduardo J. Dubuc Cc: Categories list Objet : Re: categories: subculture Dear all, I'd just like to point out that a quick google search of "category theory evil" gives the correct definition, from the nLab page. As long as articles are referenced properly, this is a non-issue. Moreover, frequently people define things in papers which remain unused outside that one article - as long as everything is clear, there is no problem here. With regards the original problem, that evil is a poor choice, I personally see little point in changing a word no one would be offended by. Ruadhaí [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Ruadhai <ruadhai@gmail.com> wrote:
With regards the original problem, that evil is a poor choice, I personally see little point in changing a word no one would be offended by.
It is certainly not the case of the work "kosher" used by some people on this list. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
It may well be, as Ruadhaí points out, that
... a quick google search of "category theory evil" gives the correct definition, from the nLab page.
But does a search for "evil" give you that, as well?
... With regards the original problem, that evil is a poor choice, I personally see little point in changing a word no one would be offended by.
The word "evil" is not a mere anagram for "live", "veil", or "vile", but has a meaning of its own, replete with connotations of opprobrium for whatever it is used as descriptive adjective for. On that ground, I would propose, it *is* a poor choice -- unless you see little point in respecting the ordinary meaning of the word "evil", or great value in offending those who would respect it. It's an excellent choice if your goal is precisely to offend those for whom "evil" already has a meaning incompatible with its proposed mathematical use here. Perhaps there are even better choices, though: Why not "demented", "testicular", "terrorist", or "gay" instead? Or some other negative word even better suited to the purpose of getting a rise out of the literal-minded, if all you really want to do with it is to "épater les bourgeois"? With dumbfounded cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Dear all, Very briefly. Many good things in mathematics are depending on the choice of a representation which is not invariant under equivalences, or under isomorphisms. Modern geometry would not exists without coordinate systems. This is true also of algebra and category theory. Algebraic structures are often described by generators and relations. Homological algebra is using non-canonical projective or injective resolutions. Choosing a base point may help computing the fundamental group of a topological space. Choosing a triangulation may help computing the homology groups. Invariant notions are often constructed from notions which are not. For example, the Euler characteristic of a space is best explaned by using a triangulation. Another example from homotopy theory: the notion of homotopy pullback square in a Quillen model category is invariant under weak equivalences, but its definition depends on the notion of pullback square which is not invariant under weak equivalences! Part of the art of mathematics is in constructing invariant notions from non-invariant ones. We should recognize the usefulness and importance of the latter. Please, let us not call them "evil"! Best, André PS: We should reserve the word "evil" to name things that really are. ------_=_NextPart_001_01CB5C66.6607A3FA Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"> <HTML> <HEAD> <META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"> <META NAME="Generator" CONTENT="MS Exchange Server version 6.5.7654.12"> <TITLE>Not invariant but good</TITLE> </HEAD> <BODY> <!-- Converted from text/plain format --> <P><FONT SIZE=2>Dear all,<BR> <BR> Very briefly.<BR> <BR> Many good things in mathematics are depending on the choice<BR> of a representation which is not invariant under equivalences,<BR> or under isomorphisms. Modern geometry would not exists<BR> without coordinate systems. This is true also of algebra<BR> and category theory. Algebraic structures are often described by<BR> generators and relations. Homological algebra is using non-canonical<BR> projective or injective resolutions. Choosing a base point may help<BR> computing the fundamental group of a topological space.<BR> Choosing a triangulation may help computing the homology groups.<BR> Invariant notions are often constructed from notions which are not.<BR> For example, the Euler characteristic of a space<BR> is best explaned by using a triangulation.<BR> <BR> Another example from homotopy theory:<BR> the notion of homotopy pullback square in a Quillen model category is<BR> invariant under weak equivalences, but its definition depends on<BR> the notion of pullback square which is not invariant under weak equivalences!<BR> <BR> Part of the art of mathematics is in constructing invariant notions<BR> from non-invariant ones. We should recognize the usefulness and<BR> importance of the latter. Please, let us not call them "evil"!<BR> <BR> Best,<BR> André<BR> <BR> PS: We should reserve the word "evil" to name things that really are.<BR> <BR> <BR> <BR> <BR> <BR> </FONT> </P> </BODY> </HTML> ------_=_NextPart_001_01CB5C66.6607A3FA-- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (5)
-
David Leduc -
Eduardo J. Dubuc -
Fred Linton -
Joyal, André -
Ruadhai