  Let $H$ and $L$ be two Hopf algebras such that their comodule categories are
monoidal equivalent. We prove that if $H$ is a twisted Calabi-Yau (CY) Hopf
algebra, then $L$ is a twisted CY algebra when it is homologically smooth.
Especially, if $H$ is a Noetherian twisted CY Hopf algebra and $L$ has finite
global dimension, then $L$ is a twisted CY algebra.
