A Clockwise 45° embedding of Categories in Lattices
April 28th, 2010 • Uncategorized
It is generally believed that Categories constitute a unified foundation for modern constructive mathematics. However a simple observation is enough to refute this claim. It is possible to take a book on category theory and rotate the pages through 45° clockwise to transform commuting diagrams into lattices diagrams. Surprisingly, despite the generality of categories the converse is not possible. No degree of rotation of lattice diagrams results in commuting diagrams to appear.
The embedding, by rotation of paper, clearly refutes contemporary claims in the foundations of mathematics. There is however the concern that after rotation the theorems become more difficult to read, and when deciphered may not necessarily apply to lattices. This concern is overcome by the pragmatic observation that readers only look at the pictures scratch their beards and encode further theorems.