Homological dimensions with respect to a semidualizing complex

Abstract

In this paper, we build off of Takahashi and White's $\catpc $-projective dimension and $\catic $-injective dimension to define these dimensions for when $C$ is a semidaulizing complex. We develop the framework for these homological dimensions by establishing base change results and local-global behavior. Furthermore, we investigate how these dimensions interact with other invariants.