 Definition: Let \(F: \mathbf{C} \rightarrow \mathbf{D}\) and \(G: \mathbf{D} \rightarrow \mathbf{C}\) be functors going in opposite directions. \(F\) is a left adjoint to \(G (G\) a right adjoint to \(F)\), denoted by \(F \dashv G\), if there exists natural transformations \(\eta : I_{\mathbf{C}} \rightarrow GF\) and \(\xi: FG \rightarrow I_{\mathbf{D}}\), such that the composites