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\title{Conventions used in the Algebraic Stacks Documents}

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\section{Comments}
\label{section-comments}

\noindent
The philosophy behind the conventions used in writing these documents is
to choose those conventions that work. In the end the precise choices we 
make here probably do not make a big difference in the resulting theory 
of algebraic stacks of finite type over the integers (or over a field, 
or over an excellent Noetherian ring). Also, perhaps the higher level
thoery is flexible enough so as to allow for different choices here, but
still we have to choose one.

\smallskip\noindent
Occasionally it will be necessary to have use notation that does not follow 
the conventions. In this case it will always be explicitly stated.

\section{Set theory} 
\label{section-sets}

\noindent
We use Zermelo-Fraenkel set theory with the axiom of choice.
See \cite{Kunen}.

\section{Categories} 
\label{section-categories}

\noindent
A category $C$ consists of a set of objects, and for each pair of objects
a set of morphisms between them. There are no set theoretic difficulties
in defining functors and natural transformations of functors. We will call
a natural transformation of functors $F \to G$ simply a morphism of functors.

\section{Algebra}
\label{section-algebra}

\noindent
In these notes a ring is a commutative ring with a $1$. Hence the
category of rings has an initial object $\mathbf{Z}$ and a final
object $\{0\}$ (this is the unique ring where $1=0$). Modules are 
assumed unitary. See \cite{E}.

\smallskip\noindent
To continue reading, 
\begin{enumerate}

\item visit the next section: Sets,
\autoref{sets-section-introduction}, or 

\item go back to the
table of contents: \url{index.html#contents}.

\end{enumerate}

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