adjunction

English

Etymology

From Latin adjunctio, from adjungere: compare French adjonction, and see adjunct.

Noun

adjunction (countable and uncountable, plural adjunctions)

2. The act of joining; the thing joined or added.
4. (law) The joining of personal property owned by one to that owned by another.
6. (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 ${\mathcal {C}}$ and ${\mathcal {D}}$. A pair of (covariant) functors $F:{\mathcal {C}}\rightarrow {\mathcal {D}}$ and $G:{\mathcal {D}}\rightarrow {\mathcal {C}}$ together with a natural isomorphism $\Phi :\operatorname {Hom} _{\mathcal {C}}(G\cdot ,\cdot )\to \operatorname {Hom} _{\mathcal {D}}(\cdot ,F\cdot )$ (where the functors are understood as bifunctors from ${\mathcal {D}}^{\operatorname {op} }\times {\mathcal {C}}$ to $\mathbf {Set}$); any of several equivalent definitions which express the same relationship (see Adjoint functors on Wikipedia.Wikipedia ). In this case $F$ is called right adjoint to $G$, and $G$ is called left adjoint to $F$; in notation, the relationship is denoted $G\dashv F$; both functors are called adjoint functors.

   Hyponyms: equivalence of categories, isomorphism of categories, Galois connection

   Meronyms: adjoint, left adjoint, right adjoint

Derived terms

• biadjunction

 

Translations

the act of joining

• Polish: adiunkcja f
• Portuguese: adjunção f

the thing joined or added

a form of similarity between a pair of categories mapped to each other by dual morphisms

• Polish: adiunkcja f

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

• Bulgarian: ^{(please verify)} съединение (bg) (sǎedinenie)