12.1.6 simplified, ft 4

Author: Marc Bezem

fields.tex

@@ -122,7 +122,8 @@ \section{Rings, abstract and concrete}
 a \emph{ring homomorphism} from $R$ to $S$ is a (group) homomorphism
 $f:\Hom(R,S)$ that preserves the multiplicative unit and 
 left and right multiplication. This means $\USymf(1_R) = 1_S$ and
-$\USymf(\USym\ell_g(h)) = \USym\ell'_{\USymf(g)}(\USymf(h))$, and
+$\USymf(\USym\ell_g(h)) = \USym\ell'_{\USymf(g)}(\USymf(h))$ for
+all $g,h:\USymR$.\footnote{Also good for $r,r'$ by coherence.}
 $\USymf(\USymr_g(h)) = \USymr'_{\USymf(g)}(\USymf(h))$.
 \end{definition}