Noun
adjunction (countable and uncountable, plural adjunctions)
- The act of joining; the thing joined or added.
- (law) The joining of personal property owned by one to that owned by another.
- (category theory) (informally) A relationship between a pair of categories that makes the pair, in a weak sense, equivalent. (formally) said to be between two categories
and
. A pair of (covariant) functors
and
together with a natural isomorphism :\operatorname {Hom} _{\mathcal {C}}(G\cdot ,\cdot )\to \operatorname {Hom} _{\mathcal {D}}(\cdot ,F\cdot )}
(where the functors are understood as bifunctors from
to
); any of several equivalent definitions which express the same relationship (see
Adjoint functors on Wikipedia.Wikipedia ). In this case
is called right adjoint to
, and
is called left adjoint to
; in notation, the relationship is denoted
; both functors are called adjoint functors.
- Hyponyms: equivalence of categories, isomorphism of categories, Galois connection
- Meronyms: adjoint, left adjoint, right adjoint
Translations
the thing joined or added
Translations to be checked