<note>

<note>
   <title>Maps out of quotients</title>
   <p>
       In almost any algebraic context, you should never try to a define a map
       directly whose domain is a quotient, rather try to find a natural way
       to invoke the first isomorphism theorem.
   </p>
 
   <p>
   For example if <m>V,W</m> are vector spaces and <m>U</m> is a subspace
   of <m>V</m>, rather than try to define a map <m>T:V/U \to W</m>,
   try instead to define a map <m>T_0:V\to W</m> whose kernel is <m>U</m>
   and image is the same as that of <m>T</m>.
   It is easier than you think and always well-defined.
   </p>
</note>