Fra\"iss\'e sequences: category-theoretic approach to universal homogeneous structures

TL;DR

This paper introduces a category-theoretic framework for understanding universal homogeneous structures, with applications across Banach spaces, linear orderings, and compact space topology.

Contribution

It presents a novel categorical approach to universal homogeneous objects, expanding theoretical tools in multiple mathematical areas.

Findings

Unified categorical framework for universal homogeneous objects

Applications to Banach space theory and topology

Enhanced understanding of structure universality and homogeneity

Abstract

We develop category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in topology of compact spaces.