The hitchhiker guide to Categorical Banach space theory. Part II

TL;DR

This paper explores advanced categorical and homological tools like Kan extensions and derived categories to deepen the understanding of Banach space theory, providing a survey of recent developments in the field.

Contribution

It introduces and discusses sophisticated categorical and homological methods applied to Banach spaces, advancing the theoretical framework in this area.

Findings

Integration of Kan extensions into Banach space theory

Development of derived categories for Banach spaces

Analysis of Abelian hearts in the context of Banach spaces

Abstract

What has category theory to offer to Banach spacers? In this second part survey-like paper we will focus on very much needed advanced categorical and homological elements, such as Kan extensions, derived category and derived functor or Abelian hearts of Banach spaces.