Are Banach spaces monadic?

TL;DR

This paper demonstrates that Banach spaces can be characterized as monadic over complete metric spaces using the unit ball functor, with a focus on the forgetful functor involving complete pointed metric spaces.

Contribution

It establishes a monadic relationship between Banach spaces and complete metric spaces, introducing a new categorical perspective.

Findings

Banach spaces are monadic over complete metric spaces.

The unit ball functor is central to this monadic relationship.

Complete pointed metric spaces are used for the forgetful functor.

Abstract

We will show that Banach spaces are monadic over complete metric spaces via the unit ball functor. For the forgetful functor, one should take complete pointed metric spaces.