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What good is a semi-model structure on algebras over an operad?

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David White
Denison University, Granville
Fri, 2016-03-11 14:00 - 15:00
MPIM Lecture Hall

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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