  We attempt to give a gentle (though ahistorical) introduction to Koszul
duality phenomena for the Hecke category, focusing on the form of this duality
studied in joint work of Achar, Riche, Williamson, and the author. We
illustrate some key phenomena and constructions for the simplest nontrivial
case of (finite) $\mathrm{SL}_2$ using Soergel bimodules, a concrete algebraic
model of the Hecke category.
