Understand
We observe that the existence of sequential and parallel composition supermaps in higher order theories of transformations can be formalised using enriched category theory.
- Encouraged by relevant examples such as unitary supermaps and layers within higher order causal categories (HOCCs), we treat the modelling of higher order physical theories with enriched monoidal categories in analogy with the modelling of physical theories with monoidal categories.
- We use the enriched monoidal setting to construct a suitable definition of structure preserving map between higher order physical theories via the Grothendieck construction.
- We then show that the convenient feature of currying in higher order physical theories can be seen as a consequence of combining the primitive assumption of the existence of parallel and sequential composition supermaps with an additional feature of linking.