Lifting accessible model structures

Richard Garner, Magdalena Kędziorek, Emily Riehl

Research output: Contribution to journalArticle

2 Citations (Scopus)
1 Downloads (Pure)

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–Kędziorek–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.

Original languageEnglish
Pages (from-to)59-76
Number of pages18
JournalJournal of Topology
Volume13
Issue number1
DOIs
Publication statusPublished - Mar 2020

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