this is my first post, so let me know if you need some more information.
I am currently studying Hopf Algebras and and exercise I have tells me to show that $f:H \rightarrow H'$ is a morphism of Hopf Algebras, given that $H, H'$ are bialgebras and $f$ is a morphism of bialgebras.
My question is, what exactly is a morphism of Hopf algebras. I can't seem to find a precise definition online. Some sources say it preserves this antipode, but I can't get my head around what this actually means.