diff -r a93bb76a8525 -r b69b09d24049 text/ncat.tex --- a/text/ncat.tex Wed Jun 16 14:33:01 2010 -0700 +++ b/text/ncat.tex Wed Jun 16 14:39:25 2010 -0700 @@ -1520,9 +1520,47 @@ More specifically, $D\to D'$ is an antirefinement if $D'$ is obtained from $D$ by gluing subintervals together and/or omitting some of the rightmost subintervals. (See Figure \ref{fig:lmar}.) -\begin{figure}[t]\begin{equation*} -\mathfig{.6}{tempkw/left-marked-antirefinements} -\end{equation*}\caption{Antirefinements of left-marked intervals}\label{fig:lmar}\end{figure} +\begin{figure}[t]$$ +\begin{tikzpicture} +\fill (0,0) circle (.1); +\draw (0,0) -- (2,0); +\draw (1,0.1) -- (1,-0.1); + +\draw [->,red] (1,0.25) -- (1,0.75); + +\fill (0,1) circle (.1); +\draw (0,1) -- (2,1); +\end{tikzpicture} +\qquad +\begin{tikzpicture} +\fill (0,0) circle (.1); +\draw (0,0) -- (2,0); +\draw (1,0.1) -- (1,-0.1); + +\draw [->,red] (1,0.25) -- (1,0.75); + +\fill (0,1) circle (.1); +\draw (0,1) -- (1,1); +\end{tikzpicture} +\qquad +\begin{tikzpicture} +\fill (0,0) circle (.1); +\draw (0,0) -- (3,0); +\foreach \x in {0.5, 1.0, 1.25, 1.5, 2.0, 2.5} { + \draw (\x,0.1) -- (\x,-0.1); +} + +\draw [->,red] (1,0.25) -- (1,0.75); + +\fill (0,1) circle (.1); +\draw (0,1) -- (2,1); +\foreach \x in {1.0, 1.5} { + \draw (\x,1.1) -- (\x,0.9); +} + +\end{tikzpicture} +$$ +\caption{Antirefinements of left-marked intervals}\label{fig:lmar}\end{figure} Now we define the chain complex $\hom_\cC(\cX_\cC \to \cY_\cC)$. The underlying vector space is