adjunction

Etymology
From, from : compare , and see.

Noun

 * 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 $$\mathcal{C}$$ 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.

Translations

 * Polish: adiunkcja
 * Portuguese: adjunção


 * Polish: adiunkcja


 * Bulgarian: