noun The act of joining; the thing joined or added.
noun The joining of personal property owned by one to that owned by another.
noun 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 a,b and y to the ring R may be denoted R[a,b,y].
noun A relationship between a pair of categories that makes the pair, in a weak sense, equivalent.
noun 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 π and π and (covariant) functors F:πβπ and G:πβπ) A natural isomorphism Ξ¦:Homπ(Gβ ,β )βHomπ(β ,Fβ ) (where the hom-functors are understood as bifunctors from πopΓπ to πππ). See Adjoint functors on Wikipedia.Wikipedia .
noun (formally, given two categories π and π and (covariant) functors F:πβπ and G:πβπ) A natural isomorphism Ξ¦:Homπ(Gβ ,β )βHomπ(β ,Fβ ) (where the hom-functors are understood as bifunctors from πopΓπ to πππ). See Adjoint functors on Wikipedia.Wikipedia .