Functors Induced by Cauchy Extension of C∗-algebras

In this paper, we give three functors P, [⋅]K and F on the category of C∗-algebras. The functor P assigns to each C∗-algebra A a pre-C∗-algebra P(A) with completion [A]K. The functor [⋅]K assigns to each C∗-algebra A the Cauchy extension [A]K of A by a non-unital C∗-algebra F(A). Some properties of these functors are also given. In particular, we show that the functors [⋅]K and F are exact and the functor P is normal exact.