Anomalies, higher symmetries, and homotopy theory I: crossed precosheaves and a nonabelian Cech construction

Symmetries of a quantum field theory or a quantum lattice model are expected to be described not by a group but by a homotopy type, whose homotopy groups are the higher symmetry groups and whose Postnikov invariants encode 't Hooft anomalies. We propose a homotopy-theoretic definition of 't Hooft an