deeper and deeper

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.