## Franklin's Notes

### Equivalence of categories

Two categories $\mathsf{C},\mathsf{D}$ are said to be equivalent iff there exist two functors $F:\mathsf{C}\implies\mathsf{D}$ and $G:\mathsf{D}\implies\mathsf{C}$ such that $FG$ and $GF$ are naturally isomorphic to the identity morphisms in the respective categories, that is, $FG\cong 1_\mathsf{C}$ and $GF\cong 1_\mathsf{D}$.