The tensor product of props was defined by Hackney and Robertson as an extension of the Boardman– Vogt product of operads to more general monoidal theories. Theories that factor as tensor products include the theory of commutative monoids and the theory of bialgebras. We give a topological interpretation (and vast generalisation) of this construction as a low-dimensional projection of a “smash product of pointed directed spaces”. Here directed spaces are embodied by combinatorial structures… Expand