Fibrantly generated weak factorization systems

TL;DR

This paper demonstrates that under Vopěnka's principle, all small projectivity classes in locally presentable categories are accessible, providing a significant insight into the structure of such categories.

Contribution

It establishes the accessibility of small projectivity classes assuming Vopěnka's principle, linking set-theoretic assumptions with category-theoretic properties.

Findings

All small projectivity classes are accessible under Vopěnka's principle.

Connects set-theoretic principles with categorical accessibility.

Provides a new perspective on the structure of locally presentable categories.

Abstract

We prove that, assuming Vop\venka's principle, every small projectivity class in a locally presentable category is accessible.