I'm on the faculty of Wellesley College, and I'm a Research Affiliate at M.I.T.
by Bill Dwyer, Myself, Dan Kan, and Jeff Smith.
This was previously titled ``Model Categories and More General Abstract Homotopy Theory, The Next Generation'', which was itself a rewrite of what was called ``Model Categories and More General Abstract Homotopy Theory''. It discusses homotopy colimits, homotopy limits, and other homotopical universal constructions in a ``homotopical category'', i.e., a category with a class of ``weak equivalences'', but not necessarily having classes of cofibrations or of fibrations.
This has been published by the AMS, and is available directly from the AMS.
This was until recently known as ``Localization of Model Categories'', and before that it was called ``Localization, Cellularization, and Homotopy Colimits''.
We define the class of ``cellular model categories'' (which includes almost all the model categories I know about) and construct the ``Bousfield localization'' of a cellular model category with respect to an arbitrary set of maps.
This requires quite a bit of work with model categories, some of it new, and some of it known to a select few but generally inaccessible to newcomers. We present the definitions and ideas of model categories from first principles, giving complete arguments in an attempt to make this accessible to those with no experience in working with model categories. (Whether we've been successful is another question, but we've made the attempt.) We've tried to separate out the parts of proofs that are really generalities about model categories and added those to Part 2. Thus, Part 2 is a comprehensive reference for many ideas used in doing homotopy theory in model categories.
This has been published by the AMS, and is available directly from the AMS.
Errata, as of September 11, 2011:
If M is a model category and Z is an object of M, then there are model category structures on the category of objects of M over Z and the category of objects of M under Z under which a map is a cofibration, fibration, or weak equivalence if and only if its image in M under the forgetful functor is, respectively, a cofibration, fibration, or weak equivalence. It is asserted without proof in "Model Categories and Their Localizations" that if M is cofibrantly generated, cellular, or proper, then so is the category of objects of M over Z. The purpose of this brief note is to fill in the proofs of those assertions and to state and prove the analogous results for undercategories.
Here are:
This is an unpublished manuscript of Chris Reedy from around 1974 that's been circulating as an increasingly faded photocopy. It's been typed into LaTeX, and the author has given permission for it to be posted on the net.
This is a LaTeX documentclass that (along with its user manual, examdoc.tex) tries to make it easy for even a LaTeX novice to prepare exams.
Specifically, exam.cls sets the page layout so that there are one inch margins all around and provides commands that make it easy to format questions (and parts of questions, and subparts of parts, and subsubparts of subparts), assign point values to the questions (or parts, etc.), create grading tables, create very flexible headers and footers, modify the margins, and include solutions that are printed only if you include the command to print them. The user manual was written in an attempt to make this all seem simple, even to the inexperienced LaTeX user.
Latest official version: Version 2.4, dated May 22, 2011.
The user manual examdoc.tex fully describes the current version, but
it doesn't flag the features that are new since version 2.3. For
that, see the comments near the beginning of the file exam.cls.
To run LaTeX on examdoc.tex, you need exam.cls. Either put exam.cls into the LaTeX inputs directory somewhere or just keep it in the current directory. If you've already got an older copy of exam.cls somewhere on your system (e.g., if you have TeXLive installed), then put this newer version into the current directory to try it out.
Betatest version:
Version 2.407beta of exam.cls, dated December 19, 2012, and
the md5sum of that file.
Changes since version 2.4:
New environment:
solutionbox
The solutionbox environment is different from the other solution environments (solution, solutionorbox, solutionorlines, solutionordottedlines, and solutionorgrid), in that
(1) The box is always printed, whether answers are being printed
or not.
(2) The argument giving the size of the box is a required
argument, not an optional argument, and so it should be enclosed
in braces, not in brackets. It can be either a length or
\stretch{number}.
(3) We make no use of the TheSolution environment; the solutionbox
environment is completely freestanding.
If answers are not being printed then only the box is printed, with nothing in it. If answers are being printed, then the solution is printed inside of the box.
Note: It's the user's responsibility to be sure that the box is large enough to hold the solution! If the solution takes up too much vertical space, then it will spill out of the bottom of the box, overwriting whatever follows the box.
New command:
\noquestionsonthispage
This command tells the \ifcontinuation and \ifincomplete commands to assume that no part of any question is on this page. This is similar to the job done by the \nomorequestions command for the pages that follow the end of all of the questions.
If you give the command \noquestionsonthispage on a page, then
(1) \ifcontinuation on that page will expand to its second
argument,
(2) \ifincomplete on that page will expand to its second
argument, and
(3) an \ifincomplete on an earlier page will not assume that a
question from that earlier page continues onto this page.
The way that this command affects the \ifincomplete command on earlier pages is as follows: If there is a page with no questions or parts or subparts or subsubparts, then the last page before that with a question (or part, etc.) would normally be deemed incomplete; if, however, the page with no questions (or parts, etc.) (along with all adjacent pages with no questions or parts etc.) has a \noquestionsonthispage command, then that last page with a question (or part, etc.) will not be deemed incomplete.
Note that if you're tempted to use this command on a page that follows the end of all of the questions, then you should probably use the command \nomorequestions instead.
It is now possible to use a parts, subparts, or subsubparts environment inside one of the solution environments (solution, solutionorbox, solutionorlines, solutionordottedlines, or solutionorgrid) without problems from multiply defined labels or having their points (if any) counted as being actual points on the exam.
New command:
\fillwithgrid{length}
New environment:
solutionorgrid
These are similar to the \fillwithlines command and the solutionorlines environment.
By default, the created grids are in black. However, if you give the commands
\usepackage{color}
\colorgrids
then the grids will be in color, by default a light gray. That default color was defined by the command
\definecolor{GridColor}{gray}{0.8}
You can change the color by redefining the color GridColor, and you can return to using black grids by giving the command
\nocolorgrids
The default grid size and grid line thickness were set by the commands
\setlength{\gridsize}{5mm}
\setlength{\gridlinewidth}{0.1pt}
You can change either or both of those by giving new \setlength commands. The period of the grid is \gridsize (both horizontally and vertically). That is, the horizontal distance from the left edge of one vertical line to the left edge of the next vertical line is \gridsize, as is the vertical distance from the top edge of one horizontal line to the top edge of the next horizontal line. Thus, each square has outer side length equal to \gridsize+\gridlinewidth.
We changed the code for the command \fillin (which had been modified in version 2.402beta) so that if only one optional argument is used, a space following that optional argument will not be ignored. We did this in such a way that the second optional argument will be recognized even when spaces appear in between the optional arguments.
We modified the command \fillin that we had created in version 2.401beta. \fillin now takes two optional arguments (and no required arguments).
\fillin can take two optional arguments, as in
\fillin[Answer][Length]
The first optional argument is the answer to be printed above the line when \printanswers is in effect; the default value is empty. That line is printed a distance of \answerclearance below the baseline.
The second optional argument is the length of the line that we print; the default value is \fillinlinelength. The value of \fillinlinelength is set with the command
\setlength\fillinlinelength{1in}
and can be changed by giving a new \setlength command.
When answers are being printed, the first optional argument is printed subject to the declarations in the argument of the last \CorrectChoiceEmphasis command. It is centered on the line unless it is too long, in which case it extends to the right of the line.
New command:
\fillin[CorrectAnswer]{width}
This is for use in fill in the blank questions. This command inserts a blank line of width ``width''. If answers are being printed and if the optional argument ``CorrectAnswer'' appears, then the optional argument is printed subject to the declarations in the argument of the last \CorrectChoiceEmphasis command, and it is printed a distance of \answerclearance above the line. It is centered on the line unless it is too long, in which case it extends to the right of the line.
"Getting up and running with AMS-LaTeX" (contained in the file amshelp.tex) is a primer on using AMS-LaTeX. It's intended for people with at least some experience using TeX, AMS-TeX, or LaTeX.
This is an attempt to get you up and running with AmS-LaTeX as quickly as possible. These instructions (along with the template file template.tex) won't be a substitute for the full documentation, but they may get you started quickly enough so that you'll only need to refer to the main documentation occasionally.
In addition to descriptions of the basics of AMS-LaTeX, there are sections with careful descriptions of the various environments for displayed mathematics, how to use Xy-pic to draw commutative diagrams, and how to use amsrefs to create a bibliography.
This is the rewrite for the current version of AMS-LaTeX (version 2.2) of the instructions I originally wrote for an early version of AMS-LaTeX. This is version 2.3, dated January 28, 2013.
Here are