Determine whether the adjunction preserves width

Determine whether the adjoint functors between persistent and cumulative temporalized spined sd-categories are width-preserving in the sense of structured-decomposition theory, and, if not, identify modified assumptions that guarantee width preservation.

Background

The temporalization framework lifts static width parameters, such as tree-width and related measures, to persistent narratives. The paper asks whether the adjunction relating persistent and cumulative narratives preserves the resulting width structure.

A positive result would provide a width-preserving bridge between the two temporal viewpoints; a negative result would require identifying additional hypotheses under which width preservation can nevertheless be obtained.