Weak saturation and weak amalgamation property

TL;DR

This paper explores the concepts of weak saturation and weak amalgamation in accessible categories, establishing conditions for their existence and uniqueness, and discusses implications for classical model theory.

Contribution

It relates weak saturation and weak amalgamation, providing new conditions for their existence and uniqueness in accessible categories.

Findings

Established sufficient conditions for weakly saturated objects

Linked weak saturation with weak amalgamation property

Discussed implications for classical model theory

Abstract

The two model-theoretic concepts of weak saturation and weak amalgamation property are studied in the context of accessible categories. We relate these two concepts providing sufficient conditions for existence and uniqueness of weakly saturated objects of an accessible category K. We discuss the implications of this fact in classical model theory.