Monadic forgetful functors and (non-)presentability for $C^{\ast }$- and $W^{\ast }$-algebras

Alexandru Chirvasitu, Joanna Ko

We prove that the forgetful functors from the categories of $C^{\ast }$- and $W^{\ast }$-algebras to Banach $\ast$-algebras, Banach algebras or Banach spaces are all monadic, answering a question…