  In this paper, we study the diagrammatic categorification of the fermion
algebra. We construct a graphical category corresponding to the one-dimensional
fermion algebra, and we investigate the properties of this category. The
categorical analogues of the Fock states are some kind of 1-morphisms in our
category, and the dimension of the vector space of 2-morphisms is exactly the
inner product of the corresponding Fock states. All the results in our
categorical framework coincide exactly with those in normal quantum mechanics.
