# 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.

## Key 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.

---
Source: https://tomesphere.com/paper/1702.08684