  To unify the quantum electrodynamics (QED) under the first principle which
brings the renormalization unartificially, we study Feynman diagrams in QED
according to the set theory and the category theory. We add the restriction on
the electromagnetic interaction that a particle can and only can interact with
particles which never interact with onself. Thus, fermiors (lines) in tree
diagrams belong to sets, but belong to proper classes when they are in five
primitive divergent diagrams. Fermiors, photons, fermior mass and charge
compose together categories in which the group product of the local U(1) group
and the propr Lorentz group is the morphism. There is the functor projecting
the category containing fermiors in tree diagrams into the category containing
fermior in divergent diagrams. Because proper classes have not the measure,
this functor avoids the restriction of the measure. It can be regarded as the
renormalization in QED and all renormalization constants have not a fixed
magnitude.
