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) Given a pair of categories ${\mathcal {C}}$ and ${\mathcal {D}}$: an anti-parallel pair of functors $F:{\mathcal {C}}\rightarrow {\mathcal {D}}$ and $G:{\mathcal {D}}\rightarrow {\mathcal {C}}$ and a natural transformation $\eta :{\mbox{id}}_{C}\rightarrow GF$ called “unit” such that for any object $A\in {\mathcal {C}}$, for any object $B\in {\mathcal {D}}$, and for any morphism $f:A\rightarrow GB$, there is a unique morphism $g:FA\rightarrow B$ such that $Gg\circ \eta _{A}=f$. (Note: there is another natural transformation called “counit” as well but its existence may be derived by theorem.) The pair of functors express a similarity between the pair of categories which is weaker than that of an equivalence of categories.

   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)