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$K$-Continuity Is Equivalent To $K$-Exactness

Otgonbayar Uuye

Abstract


Let $A$ be a $C^{*}$-algebra. It is well known that the functor $B \mapsto A \otimes B$ of taking the minimal tensor product with $A$ preserves inductive limits if and only if it is exact. $C^{*}$-algebras with this property play an important role in the structure and finite-dimensional approximation theory of $C^{*}$-algebras.

We consider a $K$-theoretic analogue of this result and show that the functor $B \mapsto K_{0}(A \otimes B)$ preserves inductive limits if and only if it is half-exact.


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DOI: http://dx.doi.org/10.7146/math.scand.a-23299

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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