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 ++++++++++++++++++++++++++++++++