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@ -2187,10 +2187,11 @@ Egli-Milner relator is not sound or complete, although its symmetrization is sou
&\iff S\;(\powf g)^\op\comp\powf f\;T
\end{align*}\qed
\end{proof}
For every relation $r\rto X\to Y$ $\emre r=\subseteq\;\emre r=\emre r\;\subseteq=\subseteq;\emre r;\subseteq$.
%\begin{prop}
% Assuming that $r\c X\rto Y$, then $\subseteq;\hat{\emre}r;\subseteq=\subseteq;\hat{\emre}r$ and $\subseteq;\hat{\emre}r=\hat{\emre}r;\subseteq$.
%\end{prop}
\begin{prop}
Assuming that $r\c X\rto Y$, then $\subseteq;\hat{\emre};\subseteq=\subseteq;\hat{\emre}$ and $\subseteq;\hat{\emre}=\hat{\emre};\subseteq$.
\end{prop}
Barr relator is a generalization of the Egli-Milner relator, where the functor is generalized.