Limit Sketches and the Universal Realization of a Limit Sketch
Johnathon Taylor

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.
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