PlanetPhysics/Category of C Algebras
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Let be two C*-algebras. Then a -homomorphism
is defined as a C*-algebra homomorphism which respects involutions, that is:
Note: If `by abuse of notation' one uses to denote both and , then any -homomorphism commutes with , i.e., .
The category whose objects are -algebras and whose morphisms are -homomorphisms is called the category of -algebras or the -algebra category.
{\mathbf Remark:} Note that homomorphisms between -algebras are automatically continuous.