  We exhibit a complete set of identities for CNOT, the symmetric monoidal
category generated by the controlled-not gate, the swap gate, and the
computational ancillae. We prove that CNOT is a discrete inverse category.
Moreover, we prove that CNOT is equivalent to the category of partial
isomorphisms of finitely-generated non-empty commutative torsors of
characteristic 2. Equivalently this is the category of affine partial
isomorphisms between finite-dimensional Z2 vector spaces.
