Definition [efr-002G]

Let \mathcal {M} be a monoidal category, and let \bullet : \mathcal {M} \times \mathcal {C} \to \mathcal {C} be an action of \mathcal {M} on another category \mathcal {C}. Then the \mathsf {Para} construction is the category \mathsf {Para}_\mathcal {M}(\mathcal {C}) where

1. Objects are objects of \mathcal {C}
2. Morphisms A \to B are tuples P \in \mathcal {M}, P \bullet A \to B up to the natural notion of isomorphism.
3. Composition is by tensoring the parameter objects and composing.