These equations are useful in reducing proofs about adjoint functors to algebraic manipulations. An analogous statement characterizes those functors with a right adjoint. Universal constructions often give rise to pairs of adjoint functors. Galois connection, which is just the same as a pair of adjoint functors. There is also a close relation to the concept of adjoint functors. The entire proof turned on the existence of a right adjoint to a certain functor. It is also called the Hermitian adjoint. The operator is not Hermitian, since itself and its adjoint are not equal. It is called "hermitian" if it is equal to its adjoint&colon; . Note that "u" automatically preserves colimits by virtue of having a right adjoint. The norm of the adjoint or transpose can be computed as follows. This defines another bounded linear operator , the adjoint of . Galois connection , where is the lower adjoint as introduced above. This identity characterizes the transpose, and is formally similar to the definition of the adjoint. A (formally) self-adjoint operator is an operator equal to its own (formal) adjoint.