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 December 17, 2006:
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 documentation file, 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 documentation was written in an attempt to make this all seem simple, even to the inexperienced LaTeX user.
Latest official version: Version 2.3, dated July 19, 2008.
The documentation file examdoc.tex fully describes the current
version, but it doesn't flag the features that are new since version
2.2. 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 teTeX installed), then put this newer version into the current directory to try it out.
Betatest version:
Version 2.307beta of exam.cls, dated June 11, 2009, and
the md5sum of that file.
Features added since the ``Official'' version 2.3:
We fixed a bug that arose only when there were cover pages and the first page of the cover pages used a different extraheadheight or extrafootheight from that used on the first page of the regular pages. The bug caused the first page of the regular pages to use the extraheadheight and extrafootheight intended only for the first cover page.
We fixed a bug that arose only when the user used a figure or table environment that floated to the top of a page. If that happened, then a full page's worth of text was placed below the figure or table, makeing the text run over the footline and off the bottom of the page.
We fixed a bug to keep page breaks from occurring inside of \makeemptybox. We also added \begingroup \endgroup for the off chance that someone was using box0 and didn't want us to change it.
We also fixed a bug in the solutionorbox environment that showed itself when the user used \stretch in the optional argument.
We rewrote the definition of \makeemptybox and the solutionorbox environment (created in version 2.303).
The argument to \makeemptybox can now be either a length, or \fill, or \stretch{number}.
The optional argument to the solutionorbox environment can also be either a length, or \fill, or \stretch{number}. If the optional argument is omitted, then no box is printed when printanswers is false.
The minimum box height is \minboxheight, whose value is set by the command
\setlength\minboxheight{.1in}
This can be changed by giving a new setlength command, but it's not likely that anyone actually wants a box of height less than .1 inch.
New command: \makeemptybox
New environment: solutionorbox
\makeemptybox takes one argument, which is a length, and it creates an empty box of width the length of the current line and of height equal to the argument. That is, the box extends from the current left margin (which depends on whether we're in a question, part, subpart, or subsubpart) to the right margin.
The solutionorbox environment is similar to the solution environment, except that if printanswers is false and an optional argument is specified, then instead of leaving that much blank space we print an empty box of that height. The optional argument must be a dimension; it can not be \fill. If the optional argument is missing or equal to 0pt, then when printanswers is false we print nothing at all.
Note: This is changed in version 2.304beta. As of that version, the argument can be either a length, or \fill, or \stretch{number}.
New commands: \numcoverpages and \totalnumpages
\numcoverpages inserts the number of pages occupied by the coverpages environment. If there is no coverpages environment, it inserts 0.
\totalnumpages inserts the sum of \numcoverpages and \numpages. Note that if there are pages preceding a coverpages environment, then those pages will not be counted by \totalnumpages.
Also: Minor bugfix. We added \relax after some \ifnum comparisons and commented out some line endings to remove, e.g., an unwanted space inserted by \ifcontinuation when the page is a continuation.
All solution, solutionorlines, and solutionordottedlines environments are now enclosed in a group, which is begun with the argument of the command
\SolutionEmphasis
the default value of which is determined by the command
\SolutionEmphasis{}
That is, the default is that nothing is inserted. For example, if the command
\SolutionEmphasis{\itshape\small}
is used, the solutions will be set in italics, in small type.
New command: \unframedsolutions
This causes solutions to be printed as normal text, without any framing or shading. Anyone using this command should use the \SolutionEmphasis command so that the solutions will be distinguishable from the rest of the exam.
This is an introduction to AMS-LaTeX intended for those at least slightly familiar with some version of TeX, AMS-TeX, or LaTeX. The hope is that by skimming through these instructions and using the template file, you'll be able to start using AMS-LaTeX without having to read the instructions.
This is the rewrite for the current version of AMS-LaTeX (version 2.2) of the instructions I originally wrote for an earlier version of AMS-LaTeX. This is version 2.1, dated June 19, 2009.
Here's