| Abstract: |
We characterize the KK-groups of G.G. Kasparov, along with the Kasparov
product KK(A,B) x KK(B,C) -> KK(A,C), from the point of view of
category theory (in a very elementary sense): the product is regarded
as a law of composition in a category and we show that this category is
the universal one with homotopy invariance, stability,
and split exactness. The third property is a weakened type of
half-exactness: it amounts to the fact that the KK-groups transform
split exact sequences of C*-algebras to split exact sequences of
abelian groups. The method is borrowed from Joachim Cuntz's apporach
to KK-theory, in which cycles for KK(A,B) are regarded as generalized
homomorphisms from A to B: the results follow from an analysis of the
Kasparov product in this light.
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