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: Since the current version (version 2.4) is so new, there isn't currently a betatest version.
Changes since version 2.3:
No longer betatest.
New environments: EnvUplevel and EnvFullwidth
The EnvUplevel environment is similar to the command \uplevel, except that \uplevel is a command taking one argument. The EnvUplevel environment has the advantage that you can include verbatim material (using, e.g., the \verb command) in the environment. (You can't include verbatim material in the argument of an \uplevel command.)
The EnvFullwidth environment is similar to the command \fullwidth, except that \fullwidth is a command taking one argument. The EnvFullwidth environment has the advantage that you can include verbatim material (using, e.g., the \verb command) in the environment. (You can't include verbatim material in the argument of a \fullwidth command.)
New document class options:
cancelspace
nocancelspace
New commands:
\cancelspace
\nocancelspace
Using the document class option cancelspace is equivalent to giving the command \cancelspace at the beginning of the file. The default is \nocancelspace. Thus, the document class option nocancelspace has no effect, but is there to avoid errors if a user is confused.
If the user uses the document class option cancelspace and if solutions are not being printed, then any space that would be added by an optional argument to the solution, solutionorbox, solutionorlines, or solutionordottedlines environments will not be added.
If solutions are being printed (because the user used the document class option answers or gave the command \printanswers), then the option cancelspace (and the command \cancelspace) will have no effect.
We fixed an obscure bug, in which if the user gives a \qformat command, in which case they shouldn't want to give a \droppoints command, but they *do* give a \droppoints command, there is an error (\padded@point@block undefined).
\qformat and \bonusqformat are now totally independent. That is: \qformat doesn't affect bonus questions, and \noqformat no longer cancels \bonusqformat.
New command: \nobonusqformat
\nobonusqformat does for \bonusqformat what \noqformat does for \qformat.
We changed the definition of \numcoverpages so that on the first run of latex (when \exam@lastcoverpage isn't yet defined), \numcoverpages will expand to
0\mbox{\normalfont\bf ??}
instead of
\mbox{\normalfont\bf ??}
so that the construction \romannumeral\numcoverpages will not generate an error on the first run of latex.
We also made changes and corrections to comments.
New commands:
\pointsinrange{rangename}
\bonuspointsinrange{rangename}
If `rangename' is the name of a grading range defined using \begingradingrange{rangename} and \endgradingrange{rangename}, then \pointsinrange{rangename} expands to the number of points in that grading range and \bonuspointsinrange{rangename} expands to the number of bonus points in that grading range.
We also changed the checkboxes and oneparcheckboxes environments so that, when solutions are being printed, a \CorrectChoice will be printed with \CorrectChoiceEmphasis (along with the \checkedchar that marks the \CorrectChoice). This brings the behavior in line with that of the choices and oneparchoices environments.
New commands:
\settabletotalpoints
\settabletotalbonuspoints
Each of those takes one argument. After giving the command \settabletotalpoints{numpoints}, any grade or point table (partial or full) will list the total points as numpoints instead of the actual total number of points in the table.
After giving the command \settabletotalbonuspoints{numbonuspoints}, any grade or point table will list the total bonus points as numbonuspoints instead of the actual total number of bonus points in the table.
These commands are intended for exams in which students are asked to do some subset of the problems, but not all of them, and so the total number of points possible is less than the sum of the points for all of the questions.
To have one of these commands affect only a single table, confine the command and the \gradetable command inside of a group, as in
\begingroup
\settabletotalpoints{100}
\gradetable[v][questions]
\endgroup
or even just
\begin{center}
\settabletotalpoints{100}
\gradetable[v][questions]
\end{center}
New user command:
\addquestionobject
This is for when some of a question spills onto the next page, but that page doesn't have any parts, subparts, subsubparts, or choices beginning on theat page (which means that the \ifincomplete command won't know that any of that question is on that page). If you say \addquestionobject at the very end of the question, it will write a questionobject to the .aux file so that \ifincomplete will work correctly. New commands used only internally:
\first@questionobject
\questionobject@pluspagecheck
These were just to clean up some of the internal code.
Bug fix: When solutions are not being printed, the solution, solutionorlines, and solutionordottedlines environments disallow pagebreaks before the environment, which can pull the last line of the question (or part, or etc.) preceding the environment onto the next page, even when leaving a rather large space before the pagebreak. We insert
\penalty 0
to allow a pagebreak before the environment. We make no change to the solutionorbox environment, since it didn't have this problem.
New commands:
\combinedgradetable
\combinedpointtable
\partialcombinedgradetable
\partialcombinedpointtable
These are similar to \gradetable, \pointable, \bonusgradetable, \bonuspointtable, \partialgradetable, \partialpointtable, \partialbonusgradetable, and \partialbonuspointtable except that these new commands list both the points and the bonus points.
\partialcombinedgradetable and \partialcombinedpointtable take one required argument, which is the name of the grading range. All four of these commands take two optional arguments, the first being either ``v'' or ``h'' and the second being either ``questions'' or ``pages''. The possibilities are thus
\combinedgradetable[v][questions]
\combinedgradetable[v][pages]
\combinedgradetable[h][questions]
\combinedgradetable[h][pages]
\partialcombinedgradetable{rangename}[v][questions]
\partialcombinedgradetable{rangename}[v][pages]
\partialcombinedgradetable{rangename}[h][questions]
\partialcombinedgradetable{rangename}[h][pages]
The defaults are ``v'' and ``questions''.
The horizontal tables have separate rows for the points and bonus points. The vertical tables have separate columns for the points and bonus points.
The default values for the words that appear in the tables are set by the commands
\chqword{Question:}
\chpgword{Page:}
\chpword{Points:}
\chbpword{Bonus Points:}
\chsword{Score:}
\chtword{Total}
\cvqword{Question}
\cvpgword{Page}
\cvpword{Points}
\cvbpword{Bonus Points}
\cvsword{Score}
\cvtword{Total:}
The words in the table can be changed by giving any of these commands with the desired word as argument.
New environment:
oneparcheckboxes
The oneparcheckboxes environment is to the checkboxes environment as the oneparchoices environment is to the choices environment. That is, each choice is begun with either a \choice or a \correctchoice command, and these will all be printed as a single paragraph. When answers are not being printed, each choice will have a label consisting of a box that the student can check, created by the argument to the last \checkboxchar command. The default value is created by the command
\checkboxchar{$\bigcirc$}
(Note the dollar signs, since \bigcirc can appear only in math mode.) When answers are being printed, then any choice created using the \correctchoice command will be labelled by the argument to the last \checkedchar command, the default value of which is created by the command
\checkedchar{$\surd$}
New command:
\bonusqformat
The \bonusqformat command takes one argument, with the same description as for the argument of the \qformat command.
If the user gives a \qformat command, then the argument of that command is used to format both questions and bonusquestions. If, after giving the \qformat command, the user gives a \bonusqformat command, then the argument of the \bonusqformat command will be used to format bonus questions.
Note: If the user hasn't given a \qformat command, then a \bonusqformat command will have no effect.
Note: If the user gives a \qformat command and a \bonusqformat command, and then later says \noqformat, then the arguments of both the \qformat and \bonusqformat commands are no longer usable. That is, if the user later on once again says \qformat, and wants the bonus questions to have a different format from the questions, then another \bonusqformat command must be given.
New environment:
checkboxes
New commands:
\checkboxeshook
\checkboxchar
\checkedchar
The checkboxes environment is similar to the choices environment, except that choices are not numbered. Instead of numbers, each choice has a label consisting of a box that the student can check, created by the argument to the last \checkboxchar command. The default value is created by the command
\checkboxchar{$\bigcirc$}
(Note the dollar signs, since \bigcirc can appear only in math mode.) When answers are being printed, then any choice created using the \correctchoice command will be labelled by the argument to the last \checkedchar command, the default value of which is created by the command
\checkedchar{$\surd$}
The list parameters used in the checkboxes environment can be customized by redefining \checkboxeshook, the default value of which is empty. (This is similar to using \choiceshook to alter the choices environment.)
We fixed a bug that caused \bonussubpart to act like \subpart and \bonussubsubpart to act like \subsubpart.
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.
"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 2.2, dated May 24, 2011.
Here's