  We present an application of the program of groupoidification leading up to a
sketch of a categorification of the Hecke algebroid --- the category of
permutation representations of a finite group. As an immediate consequence, we
obtain a categorification of the Hecke algebra. We suggest an explicit
connection to new higher isomorphisms arising from incidence geometries, which
are solutions of the Zamolodchikov tetrahedron equation. This paper is
expository in style and is meant as a companion to Higher Dimensional Algebra
VII: Groupoidification and an exploration of structures arising in the work in
progress, Higher Dimensional Algebra VIII: The Hecke Bicategory, which
introduces the Hecke bicategory in detail.
