adjunction

Meaning

1. The act of joining; the thing joined or added.
2. The joining of personal property owned by one to that owned by another.
3. 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.

Synonyms

junction

admittance

affiliation

bond

connection

connexion

insertion

interlock

joint

juncture

link

🔗

splice

symphysis

tacking

adjunct

procedural attachment

Translations

aggiunzione

adjunção

adjunción

agregació

Adjunktion

ένθεση

adjonction

insertion

aggiunta

introduzione

immissio

adjunctie

insertie

إدخال

insercion

Etymology

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