  We study perverse sheaves of categories their connections to classical
algebraic geometry. We show how perverse sheaves of categories encode naturally
derived categories of coherent sheaves on $\mathbb{P}^1$ bundles,
semiorthogonal decompositions, and relate them to a recent proof of Segal that
all autoequivalences of triangulated categories are spherical twists.
Furthermore, we show that perverse sheaves of categories can be used to
represent certain degenerate Calabi--Yau varieties.
