English

$K$-continuity is equivalent to $K$-exactness

Operator Algebras 2012-12-11 v2 K-Theory and Homology

Abstract

It is well known that the functor of taking the minimal tensor product with a fixed CC^*-algebra preserves inductive limits if and only if it preserves extensions. In other words, tensor continuity is equivalent to tensor exactness. We consider a KK-theoretic analogue of this result and show that KK-continuity is equivalent to KK-exactness, using a result of M. Dadarlat.

Cite

@article{arxiv.1211.4490,
  title  = {$K$-continuity is equivalent to $K$-exactness},
  author = {Otgonbayar Uuye},
  journal= {arXiv preprint arXiv:1211.4490},
  year   = {2012}
}

Comments

v1. 7 pages; v2. minor update

R2 v1 2026-06-21T22:40:56.292Z