ADJUNCTION

junction, adjunction

(noun) an act of joining or adjoining things

Source: WordNet® 3.1

Etymology

Noun

adjunction (countable and uncountable, plural adjunctions)

The act of joining; the thing joined or added.

(legal) The joining of personal property owned by one to that owned by another.

(category theory) Given a pair of categories $$\mathcal{C}$$ and $$\mathcal{D}$$ : an anti-parallel pair of functors $$F:\mathcal{C}\rightarrow \mathcal{D}$$ and $$G:\mathcal{D}\rightarrow \mathcal{C}$$ and a natural transformation $$\eta:\mbox{id}_C \rightarrow GF$$ called “unit” such that for any object $$A \in \mathcal{C}$$ , for any object $$B \in \mathcal{D}$$ , and for any morphism $$f:A\rightarrow GB$$ , there is a unique morphism $$g:FA\rightarrow B$$ such that $$Gg \circ \eta_A = f$$ . (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.