No, Pierre, there's no analogy like that. Running processes **in series** is composing morphisms

\[ f \colon x \to y , \quad g \colon y \to z \]

to get a morphism

\[ gf \colon y \to z . \]

We can do this in any category.

Running processes **in parallel** is tensoring morphisms

\[ f \colon x \to y, \quad f' \colon x' \to y' \]

to get a morphism

\[ f \otimes f' \colon x \otimes x' \to y \otimes y' .\]

We can do this in any [monoidal category](https://en.wikipedia.org/wiki/Monoidal_category).

None of this has anything to do with right and left adjoints!

\[ f \colon x \to y , \quad g \colon y \to z \]

to get a morphism

\[ gf \colon y \to z . \]

We can do this in any category.

Running processes **in parallel** is tensoring morphisms

\[ f \colon x \to y, \quad f' \colon x' \to y' \]

to get a morphism

\[ f \otimes f' \colon x \otimes x' \to y \otimes y' .\]

We can do this in any [monoidal category](https://en.wikipedia.org/wiki/Monoidal_category).

None of this has anything to do with right and left adjoints!