Lifting accessible model structures
| Autor: | Emily Riehl, Magdalena Kedziorek, Richard Garner |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statement (computer science)
Pure mathematics Class (set theory) 010102 general mathematics Structure (category theory) Mathematics - Category Theory Algebraic topology 16. Peace & justice 01 natural sciences Factorization system Factorization If and only if Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Algebraic Topology (math.AT) Category Theory (math.CT) 010307 mathematical physics Geometry and Topology Mathematics - Algebraic Topology 0101 mathematics Category theory Mathematics |
| Zdroj: | Journal of Topology |
| Popis: | 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. Comment: 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 |
| Databáze: | OpenAIRE |
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