Lifting accessible model structures

Abstract

A Quillen model structure is presented by an interacting pair of weak factorization systems. We prove that in the world of locally presentable categories, any weak factorization system with accessible functorial factorizations can be lifted along either a left or a right adjoint. It follows that accessible model structures on locally presentable categories - ones admitting accessible functorial factorizations, a class that includes all combinatorial model structures but others besides - can be lifted along either a left or a right adjoint if and only if an essential "acyclicity" condition holds. A similar result was claimed in a paper of Hess-Kedziorek-Riehl-Shipley, but the proof given there was incorrect. In this note, we explain this error and give a correction, and also provide a new statement and a different proof of the theorem which is more tractable for homotopy-theoretic applications.

This paper corrects an error in the proof of Corollary 3.3.4 of "A necessary and sufficient condition for induced model structures" arXiv:1509.08154

References in corpus (1)

• Injective and Projective Model Structures on Enriched Diagram Categories

Cited by in corpus (12)

• Six model categories for directed homotopy
• Homotopy theory of Moore flows (I)
• A 2Cat-inspired model structure for double categories
• A co-reflection of cubical sets into simplicial sets with applications to model structures
• Homotopy theory of Moore flows (II)
• Comparing cubical and globular directed paths
• Induced model structures for higher categories
• The enriched Thomason model structure on 2-categories
• Joyal's cylinder conjecture
• On $2$-categorical $\infty$-cosmoi
• Comparison Between Different Topological Models of Concurrency
• Shifted symplectic and Poisson structures on global quotients