ADJUNCTION

Scrabble

WWF

A(1) D(2) J(8) U(1) N(1) C(3) T(1) I(1) O(1) N(1)

NWL/TWL ✓ Collins ✓ WWF ✓

Definition

noun

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