demonstrate diagram envoronment, with separate name, counter, and ref format

The equation environment is special -- references to equations get parentheses around them. This code shows how to replicate that.

%% Make a diagram environment just like equation but with its own counter; 
%% for only one diagram at a time
\newcounter{diagcounter}
\renewcommand{\thediagcounter}{(\thesection.\arabic{diagcounter})}
\newenvironment{diag}{\begin{equation}}{ \setcounter{diagcounter}{\value{equation}-1} \refstepcounter{diagcounter} \end{equation}}

%% Diagram environment without a counter
\newenvironment{diag*}{\begin{equation*}}{\end{equation*}}

%% This makes diag follow the theorem counter
\makeatletter\let\c@diagcounter\c@thm\makeatother

%% Set crefname
\crefname{diagcounter}{Diagram}{Diagrams}