Relative sectional category revisited

Abstract

The concept of relative sectional category expands upon classical sectional category theory by incorporating the pullback of a fibration along a map. Our paper aims not only to explore this extension but also to thoroughly investigate its properties. We seek to uncover how the relative sectional category unifies several homotopic numerical invariants found in recent literature. These include the topological complexity of maps according to Murillo-Wu or Scott, relative topological complexity as defined by Farber, and homotopic distance for continuous maps in the sense of Mac\'{\i}as-Virg\'os and Mosquera-Lois, among others.