  Mathematicians love dualities. After a brief explanation of dualities, with
examples, we turn to one of the purest and most beautiful: Isbell duality. For
any category $\mathsf{C}$, this gives an adjunction between the category of
presheaves on $\mathsf{C}$, namely the functor category
$[\mathsf{C}^{\text{op}}, \mathsf{Set}]$, and the opposite of the category of
copresheaves on $\mathsf{C}$, namely $[\mathsf{C}, \mathsf{Set}]^{\text{op}}$.
