The hypertensor product is a monoidal operation on recognition fibers induced by trace concatenation in the trace category. When two traces and are concatenated to form , the hypertensor product combines their fiber algebras into a single fiber algebra for the concatenated trace.
Axiom A4 of the QCHTTopos specification defines this operation. The hypertensor product gives the topos its characteristic “hypertensor” structure — the monoidal geometry induced by trace composition.