Limit Sketches and the Universal Realization of a Limit Sketch

TL;DR

The paper introduces a universal construction for realized limit sketches using factorization systems, providing a unified framework for understanding their realizations.

Contribution

It develops a new, streamlined method to construct the universal realized limit sketch from a given limit sketch via factorization systems.

Findings

Provides a structured framework for realizations of limit sketches.

Uses factorization systems to unify classical arguments.

Facilitates understanding of limit sketch realizations.

Abstract

We construct the universal realized limit sketch associated to a given limit sketch. The construction uses factorization systems to organize the classical argument of [2], yielding a streamlined and conceptually unified formulation of the technical steps. This provides a structured framework for understanding realizations of limit sketches in terms of factorization-theoretic data.