adjunction
nounEtymology From Latin adjunctio, from adjungere: compare French adjonction, and see adjunct.
The act of joining; the thing joined or added.
Law The joining of personal property owned by one to that owned by another.
Algebra, Mathematics, Number theory, Sciences 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#91;a,b,y#93;.
- The field adjunction #92;mathbb#123;Q#125;(#92;pi) can be obtained from #92;mathbb#123;Q#125; by adjoining #92;pi to #92;mathbb#123;Q#125;.
Category theory, Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Sciences Broadly A relationship between a pair of categories that makes the pair, in a weak sense, equivalent.
Category theory, Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Sciences 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.
Category theory, Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Sciences Formal A natural isomorphism Φ: operatorname Hom_( mathcal )C(G·,·)→ operatorname Hom_( mathcal )D(·,F·) (where the hom-functors are understood as bifunctors from 𝒟^( operatorname )op×𝒞 to mathbf Set). See Adjoint functors on Wikipedia.Wikipedia .
- Derived terms
- biadjunction