adjunction
Jump to navigation
Jump to search
English
[edit]Etymology
[edit]From Latin adjunctio, from adjungere: compare French adjonction, and see adjunct.
Noun
[edit]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.
- (mathematics, chiefly algebra and number theory) The process of adjoining elements to an algebraic structure (usually a ring or field); the result of such a process.
- The ring obtained after the adjunction of the elements and to the ring may be denoted .
- The field adjunction can be obtained from by adjoining to .
- (category theory, loosely) A relationship between a pair of categories that makes the pair, in a weak sense, equivalent.
- (category theory, strictly) A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object.
- (formally, given two categories and and (covariant) functors and ) A natural isomorphism (where the hom-functors are understood as bifunctors from to ). See
Adjoint functors on Wikipedia.Wikipedia .
- Meronyms: adjoint, left adjoint, right adjoint
- (formally, given two categories and and (covariant) functors and ) A natural isomorphism (where the hom-functors are understood as bifunctors from to ). See
Derived terms
[edit]Translations
[edit]the thing joined or added
a form of similarity between a pair of categories mapped to each other by dual morphisms
|
- The translations below need to be checked and inserted above into the appropriate translation tables. See instructions at Wiktionary:Entry layout § Translations.
Translations to be checked
|
References
[edit]
Categories:
- English terms derived from Proto-Indo-European
- English terms derived from the Proto-Indo-European root *yewg-
- English terms derived from Latin
- English terms derived from French
- English lemmas
- English nouns
- English uncountable nouns
- English countable nouns
- en:Law
- en:Mathematics
- en:Algebra
- en:Number theory
- English terms with usage examples
- en:Category theory