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 Av,w=v,A w\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. See the history of this page for a list of all contributions to it.