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.