# stacks/stacks-project

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 \input{preamble} % OK, start here % \begin{document} \title{Conventions} \maketitle \phantomsection \label{section-phantom} \tableofcontents \section{Comments} \label{section-comments} \noindent The philosophy behind the conventions used in writing these documents is to choose those conventions that work. \section{Set theory} \label{section-sets} \noindent We use Zermelo-Fraenkel set theory with the axiom of choice. See \cite{Kunen}. We do not use universes (different from SGA4). We do not stress set-theoretic issues, but we make sure everything is correct (of course) and so we do not ignore them either. \section{Categories} \label{section-categories} \noindent A category $\mathcal{C}$ consists of a set of objects and, for each pair of objects, a set of morphisms between them. In other words, it is what is called a small'' category in other texts. We will use big'' categories (categories whose objects form a proper class) as well, but only those that are listed in Categories, Remark \ref{categories-remark-big-categories}. \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{Eisenbud}. \section{Notation} \label{section-notation} \noindent The natural integers are elements of $\mathbf{N} = \{1, 2, 3, \ldots\}$. The integers are elements of $\mathbf{Z} = \{\ldots, -2, -1, 0, 1, 2, \ldots\}$. The field of rational numbers is denoted $\mathbf{Q}$. The field of real numbers is denoted $\mathbf{R}$. The field of complex numbers is denoted $\mathbf{C}$. \input{chapters} \bibliography{my} \bibliographystyle{amsalpha} \end{document}