change witness of pointedness to pointing path

group.tex

@@ -950,7 +950,7 @@ \section{Homomorphisms}
 \emph{homomorphism of abstract groups}.\index{homomorphism}
 \end{remark}
 
-A slight generalization of the discussion above will be to suppose that we have a general pointed map with an arbitrary witness of pointedness
+A slight generalization of the discussion above will be to suppose that we have a general pointed map with an arbitrary pointing path
 $k_\pt : \pt_\BH \eqto k ( \pt_\BG ) $,
 not necessarily given by reflexivity.  Indeed, that works out, thereby motivating the following definition.
 
@@ -974,7 +974,7 @@ \section{Homomorphisms}
 
 We would like to understand explicitly the effect of a general homomorphism $f$ from $G$ to $H$
 on the underlying symmetries $\USymG$, $\USymH$,
-again without assuming that the witness of pointedness of $\Bf$ is given by
+again without assuming that pointing path of $\Bf$ is given by
 reflexivity.
 So we should first study how pointed maps affect loops:\marginnote{%
     \noindent\normalsize\begin{tikzpicture}
@@ -1004,8 +1004,8 @@ \section{Homomorphisms}
 \end{definition}
 
 \begin{remark}\label{rem:loops-map}
-  If $k : X \ptdto Y$ has the reflexivity path $\refl{Y_\pt}$ as its witness
-  of pointedness, then we have an identification $\loops k \eqto \ap{k_\div}$.
+  If $k : X \ptdto Y$ has the reflexivity path $\refl{Y_\pt}$ as its
+  pointing path, then we have an identification $\loops k \eqto \ap{k_\div}$.
 \end{remark}
 
 \begin{definition}\label{def:USym-hom}