categories: deeper and deeper

[Peter Freyd <pjf@saul.cis.upenn.edu>]

Vaughan writes
 
  Ok, let me dig myself in deeper by making my example more 
  complicated. Instead of  1->3, put an arrow from  i  to  j  whenever 
  i <= j <= 2i.  Now ever y i  is a square coalgebra but no  i  is a
  cubical coalgebra.

There's an arrow from  1  to  2  but none from  1*1  to  1*2.  And
when put back in you'll obtain an arrow from  1  to  3.

Even without associativity, if  A  is a  X*X  coalgebra then  A  is
an  (X*X)*X  coalgebra.