ROOM FOUR: Colored isomorphism of C*-algebras
A basic notion involved in establishing finite nuclear dimension from Z-stability in the Toms-Winter setting is colored equivalence of maps. Roughly speaking, two maps are colored equivalent if each map is approximately expressible as the finite sum of the other map conjugated by elements of the codomain algebra. In the thesis of Jorge Castillejos, this notion was used to introduce a decomposition property at the level of C*-algebras. Among other things, it was shown that any two classifiable algebras with a unique tracial state admit this decomposition. We will discuss an extension of this result in the stably finite case.