adjunction

Etymology

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

noun

1. The act of joining; the thing joined or added.
2. (law) The joining of personal property owned by one to that owned by another.
3. (category theory) Given a pair of categories 𝒞 and 𝒟: an anti-parallel pair of functors F:𝒞→𝒟 and G:𝒟→𝒞 and a natural transformation η: mbox id_C→GF called “unit” such that for any object A∈𝒞, for any object B∈𝒟, and for any morphism f:A→GB, there is a unique morphism g:FA→B such that Gg∘η_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.
   Meronyms: adjoint, left adjoint, right adjoint