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adjoint

Pronunciation: /ˈæd͡ʒ.ɔɪnt/

The English word “adjoint” has 10 meanings listed here.

adjective

  1. Used in certain contexts, in each case involving a pair of transformations, one of which is, or is analogous to, conjugation (either inner automorphism or complex conjugation).
  2. That is related to another functor by an adjunction.
  3. Having a relationship of the nature of an adjoint (adjoint curve); sharing multiple points with.

noun

  1. The transpose of the cofactor matrix of a given square matrix.
  2. Transpose conjugate.
  3. Hermitian conjugate.
  4. A functor related to another functor by an adjunction.
  5. A curve A such that any point of a given curve C of multiplicity r has multiplicity at least r–1 on A. Sometimes the multiple points of C are required to be ordinary, and if this condition is not satisfied the term sub-adjoint is used.
  6. An assistant to someone who holds a position in the military or civil service.
  7. An assistant mayor of a French commune.

Etymology

From French adjoindre (“to join”), from late 19th C; see also adjoin. Doublet of adjunct. In the case of category theory (which brings together concepts from numerous fields), the term is often confounded with adjunct and the relationship is called an adjunction. The origin of any particular usage may therefore be uncertain.

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