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 modify the margins, format questions, and create very flexible headers and footers. The documentation was written in an attempt to make this all seem simple, even to the inexperienced LaTeX user.
Latest official version: Version 2.2, dated August 14, 2004.
This is fully backward compatible with the previous non-betatest
version (version 2.01). The documentation fully describes the current
version, but it doesn't flag the features that are new since that
earlier version. 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 2.219beta of exam.cls, dated November 24, 2007, and
the md5sum of that file.
Features added since the ``Official'' version 2.2:
There can now be partial grade tables and point tables, either bonus or non-bonus.
New commands:
\partialgradetable
\partialbonusgradetable
\partialpointtable
\partialbonuspointtable
\begingradingrange
\endgradingrange
The user defines a grading range by saying
\begingradingrange{whatever}
to start the range and
\endgradingrange{whatever}
to end the range (where ``whatever'' is a name chosen by the user).
To create the table, the user says, e.g.,
\partialgradetable{whatever}[v][questions]
That is, each of \partialgradetable, \partialbonusgradetable,
\partialpointtable, and \partialbonuspointtable takes
If either or both of the optional arguments are omitted, [questions] and [v] will be used.
If the table is indexed by questions, then it will include all questions following the \begingradingrange{whatever} and preceding the \endgradingrange{whatever}.
If the table is indexed by pages, then it will include all pages with points starting with the page containing the \begingradingrange{whatever} and ending with the page containing the \endgradingrange{whatever}.
Otherwise,
\partialgradetable is similar to \gradetable
\partialbonsugradetable is similar to \bonusgradetable
\partialpointtable is similar to \pointtable
\partialbonuspointtable is similar to \bonuspointtable
Instead of appending
\the \pageinfo@commands \the \point@toks
to \everypar, we insert them into the box \@labels. This corrects the
problem that arises when a question (or part, etc.) begins with a list
environment (including verbatim, flushleft, center, flushright, and
possibly others that are implemented as trivlist environments). The
\item command in those environments throws away the previous contents
of \everypar, and so the tokens
\the \pageinfo@commands \the \point@toks
didn't get inserted where we expected. List environments *do*
preserve the contents of the box \@labels, though.
This version of exam.cls is not completely backward compatible with
older versions. The changes only affect documents in which the user
was doing something that probably should not have been done with the
older versions, though. This new version does something useful in
situations in which older versions did something not very useful:
This change introduces a change in behavior for documents in which a
question with points begins with a parts environment, so that the
points for the first part (if any) would appear on the same line as
the points for the question. In earlier versions of exam.cls, the
points for the question would not be printed if there are points for
the part that begins on the same line. In this version of exam.cls,
all points will be printed. If they're both printed in the left
margin, or both in the right margin, then they'll be printed directly
on top of one another, which is not what you want. (You can use
\pointsinmargin, \pointsinrightmargin, and \nopointsinmargin to print
them in different placees.) If points are being printed right in the
text (i.e., \nopointsinmargin), then the points for the question will
be printed *before* the label (a) for the first part is printed.
The behavior of this new version of exam.cls seems clearly preferable
to the old behavior, but it is a change!
Internal changes so that we're now compatible with calc.sty
The command \answerline now takes an optional argument. If the optional argument appears, then when \printanswers is true the argument will be printed on the answerline. When \printanswers is false, the optional argument is ignored.
When the argument is printed, it is printed with \CorrectChoiceEmphasis and it is a distance of \answerclearance above the line. The default value of \answerclearance is set with the command
\setlength\answerclearance{0.2ex}
and it can be changed with a \setlength command.
The optional argument is centered on the answer line unless it is too long, in which case it extends to the right of the answerline.
New commands:
\pointtable
\bonuspointtable
Both of these take up to two optional arguments:
The first can be either [v] or [h].
The second can be either [questions] or [pages].
These commands are similar to the commands
\gradetable
\bonusgradetable
except that the new commands print only two columns (or rows),
omitting the column (or row) for the score.
New commands:
\questionshook
\partshook
\subpartshook
\subsubpartshook
\choiceshook
These are for advanced users who want to customize the list parameters (\topsep, \partopsep, \itemsep, \parsep, etc.) for the lists that these environments create. They are all defined to be empty, but the user can change them using \renewcommand.
New documentclass option: addpoints
Using this option is equivalent to giving the command
\addpoints
at the beginning of the document.
New commands:
\bonusquestion
\bonustitledquestion
\bonuspart
\bonussubpart
\bonussubsubpart
\bonuspointsofquestion
\bonuspointsonpage
\numbonuspoints
\bonuspointpoints
\bonuspointformat
\thebonuspoints
\bonuspoints
\bonuspointname
\marginbonuspointname
\bonusgradetable
\bhqword
\bhpword
\bhsword
\bhtword
\bvqword
\bvpword
\bvsword
\bvtword
\bvpgword
\bhpgword
The commands
\bonusquestion
\bonustitledquestion
\bonuspart
\bonussubpart
\bonussubsubpart
are the same as the commands
\question
\titledquestion
\part
\subpart
\subsubpart
except that any points assigned become ``bonus points'', which by default are typeset in the form
1. (1 point (bonus))
or
1. (2 points (bonus))
If no points are assigned, then these ``bonus'' versions of the commands are equivalent to the non-bonus versions.
The command
\bonusgradetable
is analogous to the command \gradetable; it can be used in any of the four forms
\bonusgradetable[v][questions]
\bonusgradetable[h][questions]
\bonusgradetable[v][pages]
\bonusgradetable[h][pages]
and it counts only bonus points, while \gradetable counts only non-bonus points.
The commands
\bonuspointsofquestion
\bonuspointsonpage
\numbonuspoints
are analogous to the commands
\pointsofquestion
\pointsonpage
\numpoints
The remaining new commands are for customizing the appearance of bonus points and bonusgradetable. The command
\bonuspointpoints
is analogous to the command \pointpoints; it takes two arguments, the first of which will appear after 1 or \half points the second to appear after any other number of points. The default was created by the equivalent of the command
\bonuspointpoints{point (bonus)}{points (bonus)}
If, for example, you give the command
\bonuspointpoints{bonus point}{bonus points}
then bonus points will look like
1. (1 bonus point)
or
1. (2 bonus points)
(The commands \bracketedpoints, \boxedpoints, and \nobracketedpoints have the same effect on bonus points that they have on non-bonus points, and the command \marksnotpionts replaces ``point'' with ``mark'' in all of these cases.)
\bonuspointname is analogous to \pointname, and the defaults were created by the commands
\pointname{ \points}
\bonuspointname{ \bonuspoints}
(Note the intentional space in each of those commands.)
\marginbonuspointname is analogous to \marginpointname, and the default was created by the command
\marginbonuspointname{ (bonus)}
\bonuspointformat is analogous to \pointformat.
The commands for customizing the words used in \bonusgradetable are analogous to those used for customizing the words used in \gradetable, except that they begin with a ``b'':
| \bhqword | is analogous to | \hqword |
|---|---|---|
| \bhpword | is analogous to | \hpword |
| \bhsword | is analogous to | \hsword |
| \bhtword | is analogous to | \htword |
| \bvqword | is analogous to | \vqword |
| \bvpword | is analogous to | \vpword |
| \bvsword | is analogous to | \vsword |
| \bvtword | is analogous to | \vtword |
| \bvpgword | is analogous to | \vpgword |
| \bhpgword | is analogous to | \hpgword |
New commands:
\pointformat
\themarginpoints
An old command that's also useful here is
\thepoints
\pointformat: The \pointformat command allows you to change the format used to print the points. It takes one argument, and that argument becomes the command to print the points, whether the points are being printed at the beginning of the question, in the left margin (because of \pointsinmargin), in the right margin (because of \pointsinrightmargin), or dropped in the right margin at the end of the question (because of \pointsdroppedatright).
The argument to \pointformat should contain either the command
\thepoints
which expands to the number of points followed by the argument to the last \pointname command, or the command
\themarginpoints
which expands to the number of points followed by the argument to the last \marginpointname command.
For example, the command \bracketedpoints is equivalent to
\pointformat{[\thepoints]}
if points are not being printed in the margin and to
\pointformat{[\themarginpoints]}
if points are being printed in the margin.
For another example, the command \boxedpoints is equivalent to
\pointformat{\fbox{\thepoints}}
if points are not being printed in the margin and to
\pointformat{\fbox{\themarginpoints}}
if points are being printed in the margin.
For another example, if you give the commands
\pointsinmargin
\marginpointname{\%}
\pointformat{\slshape (\themarginpoints)}
then the points will be printed in the left margin, followed by the symbol `%', surrounded by parentheses, all in slanted type.
For another example, if you give the commands
\pointsinrightmargin
\marginpointname{\%}
\pointformat{\fbox{\bfseries \boldmath \themarginpoints}}
then the points will be printed in the right margin, followed by the symbol `%', all in bold and surrounded by a box. (Note: The commands \bfseries and \boldmath are needed here because the ``one half'' printed when you use half points is printed in math mode while the rest of the points are printed in text mode.)
There is a new conditional defined:
\ifprintanswers
This can be used to insert material only when answers are being printed, or only when answers are not being printed. For example, you can say
\ifprintanswers
Some stuff
\else
Other stuff
\fi
to insert ``Some stuff'' when answers are being printed or ``Other stuff'' when they're not being printed. You can also accomplish the same thing with the command
\ifthenelse{\boolean{printanswers}}{Some stuff}{Other stuff}
Thus, if you wanted to end the current page and then leave a blank page only when answers are not being printed, you could do that with either the commands
\ifprintanswers
\else
\newpage
\leavevmode
\newpage
\fi
or with the single command
\ifthenelse{\boolean{printanswers}}{}{\newpage\leavevmode\newpage}
The default method of highlighting the correct choice is boldface, but this can be customized using the \CorrectChoiceEmphasis command. The default is created by the command \CorrectChoiceEmphasis{\bfseries}, but you can override this. For example, if you give the command \usepackage{color} after your \documentclass command, then you can give the command \CorrectChoiceEmphasis{\color{red}} to have the correct choice printed in red (assuming your printer can produce this color).
There are two new commands: \titledquestion and \thequestiontitle.
\titledquestion{Question \thequestion: Concepts}
which sets the question title to ``Question 2: Concepts'' (if this is the second question) and doesn't set any pointvalues, or
\titledquestion{Design}[10]
which sets the question title to ``Design'' and sets the
pointvalue to ``10''. (Note that the question title doesn't
include the number of the question unless you put it there using
the \thequestion command.)
The title of the question then automatically replaces the question
number in a grading table indexed by question numbers.
If a question is begun with \question (instead of \titledquestion), then the value of \thequestiontitle will automatically be set to the number of the question.
Note: The contents of \thequestiontitle don't appear anywhere in the actual question unless you do something to make it appear. For example, the command
\qformat{\textbf{Question \thequestion: \thequestiontitle}\dotfill\thepoints}
would insert the number of the question along with the title of the question and the point value at the beginning of the question.
Note: If you use a grading table indexed by questions and you use the \titledquestion command, then the number of the question won't appear in the grading table unless you include \thequestion in the title of the question.
Note: If \thequestion appears in both the argument to \qformat and the title of the question, then the question number will be printed twice.
If the command \thequestiontitle is never used, then the only effect of using the command \titledquestion is that in a grading table indexed by question number, this question will be indexed by the title of the question, rather than by the question number, and the title of the question would never appear except in the grading table.
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 1.2) of the instructions I originally wrote for an earlier version of AMS-LaTeX. This is version 2.0, dated August 10, 2000.
Here's