A trace category is the small category that serves as the primitive temporal scaffold of the Quasicrystalline Hypertensor Topos. Its objects are finite sequences of abstract trace-steps, and its morphisms are admissible normalizations — finite sequences of deletion, commutation, and reassociation moves. The collection of objects forms a free partially commutative monoid on the set of trace-steps.
Axiom A0 of the QCHTTopos specification defines the trace category. It encodes the shapes along which information, geometry, or logical structure may flow, while morphisms capture when two shapes should be regarded as equivalent.