No subject

Thu Jul 5 12:38:43 CEST 2012

=C2=A0 =C2=A0 Given<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 F, a functor<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 G, a functor<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 e, a natural transformation from F to G<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (i.e., e :: forall a. F a -&gt; G=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 g, a G-algebra<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 (i.e., f :: G X -&gt; X, for some=
 fixed X)<br>
=C2=A0 =C2=A0 it follows that<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 cata g . cata (In . e) =3D cata (g . e)<br>
The proof of which is easy. So it&#39;s sufficient to be a catamorphism if =
your f =3D In . e for some e. I don&#39;t recall off-hand whether that&#39;=
s necessary, though it seems likely<span><font color=3D"#888888"><br>

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