Orwell at Typepad Yet Again
Orwell’s Government

Quantum Gravity Lesson 38

Every math undergraduate loves their torus, with the 18 triangles needed to compute homology. With quantum cubes, we automatically label axes discretely with powers of a letter. 
So when does a square include a 2-cell? Look at the bottom left square. 


A category theorist will immediately see that this is a limit diagram for the product of X and Y. But the square defined by the generator of H1 does not yield a nice square, although it does commute.