HINTS ON USING tac.cls

The style file for Theory and Applications of categories is 
based on the article style of LaTeX, and was created by 
Michael Barr and TAC authors. Thus, your TeX source code will be generally
similar to code you would produce in using the article style. The 
exceptions concern the title, abstract, proclamation of theorems, 
propositions etc., and the references. 

Your file should begin with 
\documentclass{tac}
and of course the file tac.cls must be in a directory where TeX 
looks for input.

Title, Abstract:

There are several required macros which are similar to those of LaTeX:

\title, \author, \address, \eadress, \keywords, \amsclass

you may use multiple author names and addresses - use \\ to obtain a new 
line; \amsclass refers to AMS 2020 Subject Classification.

Optional title macros are

\thanks, \dedication

note that \thanks is separate from \author (in contrast to the 
article style.) 

After \begin{document} you should include a \maketitle as usual.

There is an `abstract' environment, so the text of your abstract should 
begin with \begin{abstract} and end with \end{abstract}.

Proclamations:

These are handled using the \subsection counters and you may use
\label's as usual. The macros for proclamations come in pairs, for example

\theorem, \endtheorem

The macro pairs available are:

\theorem, \proposition, \corollary, \lemma, \definition, \remark, \example

For adding your own proclamation names, see the the journal's author 
information. 

You may find it convenient to abbreviate, for example

\let\thm\theorem
\let\endtheorem\eth

The text of proofs should begin with \proof, and end with \endproof
(the latter provides a `Halmos bar'.)

References:

The reference list environment begins with

\begin{references} or \begin{references*} 

depending on whether the Harvard e.g. [Eileberg-Mac Lane, 1945] or a 
numerical reference style is used. You may substitute 

\references, \references*

closed with \endreferences(*) for the environment declaration.

Finally, the style files ends with some useful macros for dealing with 
new math operations, math roman elements like `hom' and multi-line displays.