category of C*-algebras
Definition 0.1
Let

be two C*-algebras. Then a
-homomorphism

is defined as a
C*-algebra
homomorphism

which respects involutions, that is:

for any
Note:
If `by abuse of notation' one uses
to denote both
and
,
then any
-homomorphism
commutes with
, i.e.,
.
Definition 0.2
The category

whose objects are

-algebras and whose morphisms are

-homomorphisms is called the
category of
-algebras or the

-algebra category.
Remark:
Note that homomorphisms between
-algebras are
automatically continuous.
-
- 1
-
Kustermans, J., C*-algebraic Quantum Groups arising from Algebraic Quantum
Groups, Ph.D. Thesis, K.U.Leuven, 1997.
- 2
-
Sheu, A.J.L., Compact Quantum Groups and Groupoid C*-Algebras, J. Funct.
Analysis 144 (1997), 371-393.
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