Several years ago, Loring, Pedersen and I proved semiprojectivity for a class of C*-algebras arising as mapping tori for maps between finite-dimensional C*-algebras. We did this to address a class of matrix approximation problems in the spirit of Lin and Friis-Rrdam, and consequently did not publicize the semiprojectivity result much in itself.

In recent years, the classification community has been working intensely with the class of subhomogeneous C*-algebras, overlapping nontrivially with the class considered in our work, and I have noted a couple of instances were our result could have been used to simplify certain arguments. Thus I intend to try to promote our old result and give an overview of its rather complicated proof.