adjunction

{{category theory}} A form of similarity between a pair of categories <math>\mathcal{C}</math> and <math>\mathcal{D}</math> which is weaker than equivalence, which in turn is weaker than isomorphism. Given functors <math> F:\mathcal{C} \rightarrow \mathcal{D} </math> and <math> G:\mathcal{D} \rightarrow \mathcal{C} </math>, ''F'' is "left adjoint" of ''G'', and ''G'' "right adjoint" of ''F'', denoted as <math> F \dashv G </math>, if