forked from stacks/stacks-project
-
Notifications
You must be signed in to change notification settings - Fork 0
/
conventions.tex
71 lines (51 loc) · 1.76 KB
/
conventions.tex
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
\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}