2. Noun.  (category theory) A form of similarity between a pair of categories $mathcal\left\{C\right\}$ and $mathcal\left\{D\right\}$ which is weaker than equivalence, which in turn is weaker than isomorphism. Given functors $F:mathcal\left\{C\right\} ightarrow mathcal\left\{D\right\}$ and $G:mathcal\left\{D\right\} ightarrow mathcal\left\{C\right\}$, ''F'' is "left adjoint" of ''G'', and ''G'' "right adjoint" of ''F'', denoted as $F dashv G$, if .