In general, it is difficult to transfer a model structure from a monoidal

model category M to the category of algebras over a (colored) operad P in M.

Often, one only ends up with a semi-model structure (i.e. where half the

factorization and lifting axioms only hold for maps with cofibrant domain),

and even this traditionally requires P to be Sigma-cofibrant. I?ll explain

what standard techniques still work in the context of semi-model categories,

so that users of model categories can get by if they only have a semi-model

structure. I?ll then report on recent joint work with Donald Yau providing

model structures and semi-model structures for algebras over non-cofibrant

colored operads. As an application, we?ll prove a very general result

regarding preservation of algebras by left and right Bousfield

localizations. Examples will include spaces, spectra, equivariant spaces and

spectra, categories, chain complexes, and the stable module category.

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