On the construction of functorial factorizations for model categories

Abstract

We present general techniques for constructing functorial factorizations appropriate for model structures that are not known to be cofibrantly generated. Our methods use "algebraic" characterizations of fibrations to produce factorizations that have the desired lifting properties in a completely categorical fashion. We illustrate these methods in the case of categories enriched, tensored, and cotensored in spaces, proving the existence of Hurewicz-type model structures, thereby correcting an error in earlier attempts by others. Examples include the categories of (based) spaces, (based) G-spaces, and diagram spectra among others.

Final journal version to appear in Algebraic & Geometric Topology with improvements suggested by the referee

References in corpus (4)

• Understanding the small object argument
• Algebraic model structures
• Homomorphisms of higher categories
• Cofibrantly generated natural weak factorisation systems

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• Algebraic weak factorisation systems I: accessible AWFS
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• The Coalgebraic Structure of Cell Complexes
• Six model categories for directed homotopy
• Homotopy homomorphisms and the classifying space functor
• Equivariant infinite loop space theory, the space level story
• Comparing cubical and globular directed paths
• Monoidal algebraic model structures
• Cylindrical model structures
• Bousfield localisation and colocalisation of one-dimensional model structures
• Recognition of commutative algebra spectra through an idempotent quasiadjunction