Examples of monoidal

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Most of the definition is a routine generalisation of that of monoidal functor.
For readability, and without loss of generality, we consider strict monoidal categories.
The key to the proof is the following observation about monoidal categories.
However, their formalism demands the presence of considerably more structure, which includes the requirement of being monoidal closed (actually -autonomous).
Likewise, for the symmetric monoidal case we have an alternative (intuitive) characterization for the auxiliary tiles of cartesian double categories.
Another possibility might be to extend our investigation to non-strict monoidal structures.
Of course, the same holds for any other symmetric strict monoidal category.
So we must complete and with suitable values to obtain satisfactory monoidal product and lattice meet operators.
In doing so, semantics reformulates in its own language (cartesian or monoidal closed categories) problems traditionally seen as syntactical, such as abstract machines and complexity.
So there should be a gain in finding for the calculus mentioned above a new, self-contained, completeness proof with respect to symmetric monoidal closed isomorphisms.
However, this is not the case: there are net morphisms that cannot be extended to symmetric monoidal functors between the respective categories of processes.
For simplicity, we assume that the monoidal structure is strictly associative and unitary.
A model is a single category with: a monoidal biclosed structure; a symmetric monoidal closed structure; a cartesian closed structure.
Moreover, the axiomatization of symmetric monoidal and cartesian double categories seems to characterize precisely concurrent tile computations.
An important point to note is that we always assume that the monoidal category structure is strict.

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