On the uniqueness of cellular injectives

TL;DR

This paper presents a category-theoretic framework using weak factorization systems and the fat small object argument to analyze the uniqueness of certain injective structures like Boolean algebras and Banach spaces.

Contribution

It offers a unified categorical approach to the existence and uniqueness of cellular injectives, extending previous results in Boolean algebras and Banach spaces.

Findings

Unified categorical framework for injective structures

Application of weak factorization systems and fat small object argument

Clarifies conditions for uniqueness of cellular injectives

Abstract

A. Avil\'es and C. Brech proved a intriguing result about the existence and uniqueness of certain injective Boolean algebras or Banach spaces. Their result refines the standard existence and uniqueness of saturated models. They express a wish to obtain a unified approach in the context of category theory. We provide this in the framework of weak factorization systems. Our basic tool is the fat small object argument.