Breaking up 'properties' in the intro into smaller subsections, converting many properties back to theorems, and numbering according to where they occur in the text. Not completely done, e.g. the action map which needs statements made consistent.
%!TEX root = ../blob1.tex
%%%%% excerpts from KW's include file of standard macros
%%% (with various new ones added)
\def\z{\mathbb{Z}}
\def\r{\mathbb{R}}
\def\c{\mathbb{C}}
\def\t{\mathbb{T}}
\def\ebb{\mathbb{E}}
\def\k{{\bf k}}
\def\du{\sqcup}
\def\bd{\partial}
\def\sub{\subset}
\def\subeq{\subseteq}
\def\sup{\supset}
%\def\setmin{\smallsetminus}
\def\setmin{\setminus}
\def\ep{\epsilon}
\def\sgl{_\mathrm{gl}}
\def\op{^\mathrm{op}}
\def\deq{\stackrel{\mathrm{def}}{=}}
\def\pd#1#2{\frac{\partial #1}{\partial #2}}
%\def\lf{\overline{\cC}}
\def\lf{\cC}
\def\ot{\otimes}
\def\vphi{\varphi}
\def\inv{^{-1}}
\def\ol{\overline}
\def\spl{_\pitchfork}
%\def\nn#1{{{\it \small [#1]}}}
\def\nn#1{{{\color[rgb]{.2,.5,.6} \small [#1]}}}
\long\def\noop#1{}
% equations
\newcommand{\eq}[1]{\begin{displaymath}#1\end{displaymath}}
\newcommand{\eqar}[1]{\begin{eqnarray*}#1\end{eqnarray*}}
\newcommand{\eqspl}[1]{\begin{displaymath}\begin{split}#1\end{split}\end{displaymath}}
% tricky way to iterate macros over a list
\def\semicolon{;}
\def\applytolist#1{
\expandafter\def\csname multi#1\endcsname##1{
\def\multiack{##1}\ifx\multiack\semicolon
\def\next{\relax}
\else
\csname #1\endcsname{##1}
\def\next{\csname multi#1\endcsname}
\fi
\next}
\csname multi#1\endcsname}
% \def\cA{{\cal A}} for A..Z
\def\calc#1{\expandafter\def\csname c#1\endcsname{{\mathcal #1}}}
\applytolist{calc}QWERTYUIOPLKJHGFDSAZXCVBNM;
% \DeclareMathOperator{\pr}{pr} etc.
\def\declaremathop#1{\expandafter\DeclareMathOperator\csname #1\endcsname{#1}}
\applytolist{declaremathop}{pr}{im}{gl}{ev}{coinv}{tr}{rot}{Eq}{obj}{mor}{ob}{Rep}{Tet}{cat}{Maps}{Diff}{Homeo}{sign}{supp}{Nbd}{res}{rad}{cell};
\DeclareMathOperator*{\colim}{colim}
\DeclareMathOperator*{\hocolim}{hocolim}
\DeclareMathOperator{\most}{most}
\DeclareMathOperator{\rest}{rest}
\DeclareMathOperator{\kone}{cone}
%%%%%% end excerpt