#
nLab
adjoint

## In linear algebra

The term *adjoint* originates in linear algebra, where it may refer, in increasing generality, to:

## In category theory

In category theory, the term “adjoint” foremost refers to “adjoint functors”, a terminology which is probably inspired by the similarity between the characteristic hom-isomorphism of such functors and the defining equality $\big\langle A v ,\, w \big\rangle
\,=\, \big\langle v ,\, A^\dagger w \big\rangle$ for Hermitian adjoint linear operators.

Proceeding from here, there are various variants of adjointness in category theory:

Last revised on May 8, 2023 at 03:20:01.
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