Definitions from Wiktionary (adjunction)

▸ noun:  The act of joining; the thing joined or added.
▸ noun:  (law) The joining of personal property owned by one to that owned by another.
▸ noun:  (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.
▸ noun:  (category theory, loosely) A relationship between a pair of categories that makes the pair, in a weak sense, equivalent.
▸ noun:  (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.
▸ noun:  (formally, given two categories 𝒞 and 𝒟 and (covariant) functors F:𝒞→𝒟 and G:𝒟→𝒞) 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.





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