Definition 1.2.9 (Equivalence of Categories).label Let $\frak{C},\frak{D}$ be categories then we say they are equivalent (resp. antiequivalent) if there are covariant (resp. contravariant) functors $F:\frak{C}\to \frak{D}$ and $G:\frak{D}\to \frak{C}$ such that $G\circ F\iso \indi{\frak{C}}$ and $F\circ G\iso \indi{\frak{D}}$.