Dualities originally appear in monoidal categories; but they can be defined in other contexts. We can define dualities in a linearly distributive category, dualities in a bicategory, dualities in a duoidal category, or dualities in a Physical monoidal multicategory.
- When all the objects of a symmetric monoidal category have duals, we say that the category is a compact closed monoidal category.
- A duality in the bicategory of categories is an adjunction.