equivalence of categories

Let \(\mathcal{C}, \mathcal{D}\) be categories, \(\mathcal{F}: \mathcal{C} \rightarrow \mathcal{D}\) and \(\mathcal{G}: \mathcal{D} \rightarrow \mathcal{C}\) be functors.

Then \(\mathcal{F},\mathcal{G}\) together with natural isomorphisms \(\eta: \mathcal{F} \circ \mathcal{G} \rightarrow \mathrm{id}_{\mathcal{D}}\) and \(\epsilon: \mathcal{G} \circ \mathcal{F} \rightarrow \mathrm{id}_{\mathcal{C}}\)