A 2-adjunction is a common name for various kinds of adjunctions in 2-category theory; not only adjunctions between 2-categories themselves, but more generally adjunctions within an arbitrary 3-category. Since there are various different levels of strictness at which one works in 2-category theory, there are various different kinds of 2-adjunction, including:

There are also more specialized kinds of 2-adjunction, such as

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