As "task coordinator" for commutative diagrams in the LaTeX 3 project, I would be grateful if you would turn your minds to the question of the idiom in which you think it is best to express the majority of diagrams in the main stream of category theory and other parts of algebra. The extremes are not a good test of this: (1) for diagrams which are just a square or just a triangle, it makes no difference what package you use, because you can always add \square and \triangle macros on top of it. Mike did that for LaTeX pictures, and anyone moderately competent in writing TeX macros could do it for any of the graphics packages. I don't think there's any utility in it but others may do. (2) if you are writing about the foundations of the theory of braids, by definition you are doing something which is novel, peculiar and not main-stream, and necessarily this will involve ad hoc methods of creating your graphics. The low-level ad-hoc-ery needed for this is a BURDEN to the use and development of tools for idiomatic uses. The matrix syntax has been used by several macro designers, including Kris Rose (who, as he acknowledges, took it from me) for XY-PIC, Francis Borceux, Mike Spivak (lamstex) and me. In one form or another I think this has proved to be very useful. Mike Barr refuses to say anything that might be interpreted as approval for my package, but everyone else who has actually used TeX for commutative diagrams seems to agree. In my report to the LaTeX 3 project may I say that that is the consensus of the category theory community? Paul PS The current version of my package emulates AMSTEX (not lamstex). That is, you can take your existing amstex document, add \input diagrams \diagramstyle[amstex] and it will replace the amateurish mess by some pretty diagrams. anonymous FTP theory.doc.ic.ac.uk /tex/contrib/Taylor/tex/diagram* +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Paul writes:
Mike Barr refuses to say anything that might be interpreted as approval for my package, but everyone else who has actually used TeX for commutative diagrams seems to agree.
...about Paul's package... I have used it. I don't find his syntax helpful, intuitive, or sufficiently extensible. I do not feel that the best interest of the community would be served by Paul's syntax becoming the standard, and will communicate this (as a minority view) to the LaTeX 3 project. David. ++++++++++++++++++++++++++++++++++++
Paul Taylor has consistantly refused to reply to my comments regarding the design of a diagrams package for LaTeX 3. I can only suspect that this is because to acknowledge the use of diagrammatic algebra in such roles as Feynman diagrams, proof-nets, knot and braid theory, the representation theory of quantum groups, etc. would completely undermine his position, which seems limited to those sorts of diagrams used by categorists interested in *logical* applications of 1-category theory only. I take strong exception to his remark
(2) if you are writing about the foundations of the theory of braids, by definition you are doing something which is novel, peculiar and not main-stream, and necessarily this will involve ad hoc methods of creating your graphics. The low-level ad-hoc-ery needed for this is a BURDEN to the use and development of tools for idiomatic uses.
which shows a peculiar notion of the main-stream. The portion of category theory which has had the most fruitful interactions with the main-stream of mathematics *as a whole* has of late been the part which uses braid diagrams. In answer to Paul's question:
In my report to the LaTeX 3 project may I say that that is the consensus of the category theory community?
*NO* not if you ask me. Not to be wholely negative, I want to point out that the suggestion of a syntax allowing one to specify a size of matrix, locations of text at matrix nodes (usually objects), starting and endings of arrows (and labelling text), and (for 2-categorists) labels (including short arrows and text) for regions, would in fact permit one to specify knot diagrams, Feynman diagrams, proof-nets, etc. if one had the options of a. specifying (in place of text) various sorts of nodes (trivalent vertex, overcrossing, undercrossing, box with text, empty circle, etc.) b. specifying various types of connections (arrow, line, wavy line, semicircular arc on either side of the line, etc.) Similarly such syntax would be perfectly adequate for pentagonal, hexagonal, etc. diagrams unless one demands regular polygons. Personally, I a quite happy with hexagons with two right angle and four of 3\pi/4. --David Yetter +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Subject: commutative diagrams (several posts) Note from moderator: Several posts on the topic of the moment follow. I regret that Charles Wells' was delayed until today. I would like to thank Michelle Boers for helping with sending out posts during my absence from telnet facilities. The posts which follow have been slightly edited for heat. If anyone wishes the changes restored, let me know. Bob Rosebrugh ++++++++++++++++++++++++++++++++
A small side-issue relating to commutative squares concerns introduction of a standard notation for pull-backs and push-outs. In my Pitman book (Research Notes #56) I introduced the following symbols in the middle of the square. For a pull-back, use a small square with upper and left-hand edge removed but top left vertex intact. "Dually" for push-out. TEXperts will know how to encode this. These symbols have found some following among topologists (perhaps by default). No doubt your more ardent correspondents will wish to comment. Jon Berrick. ++++++++++++++++++++++++++++++++++++
To reply to David Yetter's "not being entirely negative", I myself suspected that the matrix notation with special nodes for over/undercrossings (such as \HonV and \VonH) would extend to braids and the like. Maybe those who consider them to be so important conceptually would spend a few minutes thinking out how to express braids in a matrix notation ... BTW I can't readily quote you or edit my own text, because I'm working on a dumb terminal 500km from home. The over and undercrossings of horizontal and vertical lines have been in my package for ages. There's also some kind of "break" feature in xypic. If you care to look in the international TeX archive, you will find macro packages intended for drawing Feynmann diagrams and trees. There are also prototypes of mine for proof trees and natural deduction proof boxes, and many other things. No one package is ever going to do all of the jobs, and nor should it: if you want wysiwyg, use a pen an paper. Paul +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
participants (4)
-
David Murphy -
dyetter＠math.ksu.edu -
Jon Berrick -
Paul Taylor