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We construct a functor from the Hecke category to a groupoid built from theunderlying Coxeter group. This fixes a gap in an earlier work of the authors.This functor provides an abstract realization of the localization of the Heckecategory at the field of fractions. Knowing explicit formulas for thelocalization is a key technical tool in software for computations with Soergelbimodules.

Localized calculus for the Hecke category