Examples of adjoint

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A 2-category is said to be compact, if every 1-cell has both a left and a right adjoint.
Both left and right adjoint provide a mechanism for storing this information.
The functor is a right adjoint, and thus preserves all limits.
Then the upper adjoint of f equals the interior of f (provided that f exists).
Similarly, a function has a lower adjoint if and only if it is universally conjunctive, and lower adjoints are also unique.
The adjoint eigenfunctions k given by (2.7) do not change sign.
This particularly involves the approximation of the 'adjoint solution'.
In order to transform equation (27), we introduce the classical adjoint state.
As already calculated before, the adjoint operator is not - - completely operating at a homogeneous level in (z, z), but also introduces terms of higher - degree.
Note that (2.16a) and (2.16b)are adjoint to each other, and thus they have conjugate eigenvalues and the same number of eigensolutions.
Here the right adjoint unfolds a transition graph into the synchronisation forest of all the possible finite runs of the system.
Note that the notions of adjoint and weakly adjoint functor coincide if the codomain is a category.
As complex interpolation is often understood in the frame of the domain of self-adjoint operators, we shall prove the following proposition.
We find that minimisation is adjoint to the inclusion of the minimised labelled graphs.
The previous constructions generalize to (not necessarily self-adjoint) affiliated operators as follows.

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