A new model for pro-categories

TL;DR

This paper introduces a new, more convenient model for pro-categories, demonstrating its usefulness through applications including solving an open problem about functorial factorizations and correcting an error in existing literature.

Contribution

The paper proposes a novel construction for pro-categories that simplifies certain operations and addresses an open problem in the field.

Findings

Provides a new model for pro-categories that is easier to work with.

Solves an open problem regarding functorial factorizations in the strict model structure.

Corrects an error in a standard reference on pro-categories.

Abstract

In this paper we present a new way to construct the pro-category of a category. This new model is very convenient to work with in certain situations. We present a few applications of this new model, the most important of which solves an open problem of Isaksen [Isa] concerning the existence of functorial factorizations in what is known as the strict model structure on a pro-category. Additionally we explain and correct an error in one of the standard references on pro-categories.