  In this note, we introduce a class of cell decompositions of PL manifolds and
polyhedra which are more general than triangulations yet not as general as CW
complexes; we propose calling them PLCW complexes. The main result is an analog
of Alexander's theorem: any two PLCW decompositions of the same polyhedron can
be obtained from each other by a sequence of certain "elementary" moves.
  This definition is motivated by the needs of Topological Quantum Field
Theory, especially extended theories as defined by Lurie.
