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Direct proofs of properties and structures of model structures for (∞, 1)-categories

Women in Topology November 29, 2017 - December 01, 2017

November 30, 2017 (09:15 AM PST - 09:45 AM PST)
Speaker(s): Julie Bergner (University of Virginia)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC



There are many different models for (∞,1)-categories, each of which has an associated model category. Given these model structures, we’d like to know what additional properties they possess, for example, which are simplicial, cartesian, or left or right proper? We know several of these results, but not all; and in particular there are not always counterexamples in the literature for when a model structure does not have a desired property. Furthermore, some of these properties are known from very general results, and it would be nice to have a more concrete proof for a given model category. In this project, we’ll seek to fill in some of these gaps in our knowledge. 



Reading List: 

• J. Bergner, “A survey of (∞, 1)-categories” In: Baez, J., May, J.P. (eds) Towards Higher Categories, Vol. 152. Springer, NY. 

• P. Hirschhorn, Model Categories and their Localizations, for background on sim- plicial, monoidal, proper model categories. 

30202?type=thumb Bergner Notes 200 KB application/pdf Download
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