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Foundations of (∞, 2) -category theory

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

November 30, 2017 (11:15 AM PST - 11:45 AM PST)
Speaker(s): Emily Riehl (Johns Hopkins University)
Location: MSRI: Simons Auditorium
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Work of Joyal, Lurie and many other contributors can be summarized by saying that ordinary 1-category theory extends to (∞,1)-category theory: that is, there exist homotopical/derived analogs of 1-categorical results. As “brave new algebra” grows in influence, many areas of mathematics now require homotopical/derived analogs of 2-categorical results and this work largely remains to be done in a rigorous fashion.  In my talks, I will give an overview of the development of (∞, 1)-category theory in the quasi-categorical model and describe the main idea behind the proof that this theory is “model independent.” I’ll then suggest some models of (∞, 2)- categories that might prove fertile for studying extensions of 2-category theory and sketch a possible strategy to demonstrate model independence.

Reading List:

  • J. Lurie “(∞, 2)-categories and the Goodwillie Calculus I”, October 8, 2009. 
Available from http://www.math.harvard.edu/∼lurie/papers/GoodwillieI.pdf. 

  • D. Gaitsgory and N. Rozenblyum , Appendix A of A study in derived algebraic geometry, Mathematical Surveys and Monographs, Vol. 221 (2017), pp. 419 - 524.
Available from http://www.math.harvard.edu/∼gaitsgde/GL/. 

  • G. M. Kelly “Elementary observations on 2-categorical limits”, Bull. Austral. Math. Soc., Vol. 39 (1989), pp. 301-317.

Potential participants should skim bits of the first two, but need not read either in full. 

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