# Commutative Diagrams in TeX

### Paul Taylor

### September 1992

## Message sent to registered users in September 1992

This message brings news of the development of my TEX package for drawing "commutative" diagrams, which is now widely used in the category theory and theoretical computer science communities. It is being sent directly to all of the users I know of (who have requested it by electronic mail or FTP from me, or asked questions about it), but as I know the package has been passed on, I would be grateful if you would copy this message to anyone to whom you have given the package itself.
The package was originally advertised on the "types" and "categories" electronic mailing lists in July 1990. In the following eighteen months some fixing of bugs took place, but there was little substantial change.
Since April 1992, I have re-written most of the code, largely with a view to improving the geometrical layout of the diagrams. Before completing this work and calling it version 4, I would like some feedback from users.
One of the areas which I have neglected in the past (largely because TEX makes it so difficult) is diagonal arrows. The code for drawing these using LATEX line segments has been re-written: now the closest available slope is chosen automatically and the commands have names similar to the horizontals and verticals.
However to do a better job of diagonals (and in future to support curved lines) some extension to TEX is needed. Being extensions they are necessarily not standard. Three possibilities are:

- additional fonts (as, for example, used by Spivak's Lamstex). However my experience of design-size fonts and linear logic symbols suggests that for users without expert knowledge or control of their local TEX systems this is more trouble than it's worth.
- PostScript is, I believe, now almost universally used as the language in which TEX documents are sent to a printer. PS commands can be embedded in DVI files and incorporated in the PS translation without extra system or user files or any user intervention. This is to some extent dependent on which DVI®PS translator is used. In the new version this is exploited in an option to implement diagonals by rotating horizontals, which works with Tomas Rokicki's "dvips".
- TPIC is a graphics extension of TEX which uses a simpler set of embedded commands. These can be used to draw diagonal lines and curves but not to perform rotations; they are, however, understood by Vojta's "xdvi" as well. Another option in the new version uses these to draw diagonal lines.

Besides diagonals, the code for adjusting horizontal and vertical arrows has been completely rewritten and does a much better job of the geometry. Many of the problems with alignment, positioning and gaps have been fixed automatically, and greater control is given to the user to adjust those which cannot be. There are also several new options for the placement of the finished diagram on the page.
Arrow commands are now declared in a much simpler way. The declaration

     \newarrow{CrossedInto}{hook}-+->

is now all that is needed to define the example `\rCrossedInto` in the manual, along with the corresponding left, down, up and diagonal commands. Another option makes a consistent selection of arrowheads for all arrows, from a choice of vee, LaTeX, curlyvee, triangle and blacktriangle.
So much for selling you the new version. The reason for mailing you and asking for comments before completing what I intend to do for version 4 is that I want to get feedback on the following questions:

- Can you use FTP (file transfer protocol)? This is the easiest method of distribution for me and for you, and there is now a huge volume of public domain software available by this method. My archive is called `ftp.dcs.qmw.ac.uk` and the diagrams package is in the directory /pub/tex/contrib/pt/diagrams. Please try to fetch the new version and manual by this method.
- If you can't use FTP, and your electronic mail passes via non-ASCII machines (particularly BITNET), what characters tend to get corrupted? The new version uses a restricted character set to avoid this problem.
- Do you have available for printing final copy a printer which understands Adobe PostScript, for example an Apple or Sun laserwriter? Who is the author of the DVI-> PS translation program you use? Please fetch the new version, try the PostScript option and tell me if you have any difficulty printing. (You may have to change the `\verbatim@ps@special` macro if you don't use Rokicki's dvips: if so, please send me details.) You can preview with a PS previewer such as PageView under OpenWindows or GhostView/GhostScript under Xwindows.
- Do your DVI translators and previewers understand TPIC `\special`s (as used in eepic.sty)? Please try the TPIC option. I would like to know whether it is worth putting effort into PostScript, TPIC or some other method.
- Have you defined your own arrow commands using `\HorizontalMap`, `\VerticalMap` or `\DiagonalMap`? Please use "grep alMap *.tex *.sty" or some similar command to find out, and tell me if you have used any components other than those in the source of version 3. It is in your interests to do this, because `\newarrow` defines arrow commands in a different way.
- Please tell me if you have any difficulty adapting to the new version, or any general comments about doing so which might be of benefit to other users.
- Other comments: have you used other packages for drawing diagrams? Do you have applications for my package other than the categorical diagrams for which it was designed? What do you see as the major limitations of the package? What persuaded you to use it, or not to use it?