# 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.

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