arXiv 1802.098892018-02-27math.CTmath.AT

Lifting accessible model structures

Richard Garner, Magdalena Kedziorek, Emily Riehl

备注：: 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
发表信息：: J. Topology 13(1) March 2020 Pages 59-76
DOI：: 10.1112/topo.12123

英文摘要：

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.

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