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Tuesday, April 7, 2015

**Abstract:** We will begin with an overview of an old problem, due to Baez and Dolan, and discuss where in the solution of this problem model category theoretic considerations arise. This requires placing left proper model structures on algebras over certain colored operads. We will discuss how this can be accomplished. Our path will take us through a discussion of model structures on commutative monoids and non-reduced symmetric operads, as well as a new filtration due to Batanin and Berger.