TY - JOUR AU - Uuye, Otgonbayar PY - 2016/03/07 Y2 - 2024/03/29 TI - $K$-Continuity Is Equivalent To $K$-Exactness JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 118 IS - 1 SE - Articles DO - 10.7146/math.scand.a-23299 UR - https://www.mscand.dk/article/view/23299 SP - 95-105 AB - <p>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. </p><p> 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.</p> ER -