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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
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC


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. 

30205?type=thumb Riehl Notes 178 KB application/pdf Download
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H.264 Video 4-Riehl.mp4 211 MB video/mp4 rtsp://videos.msri.org/data/000/030/135/original/4-Riehl.mp4 Download
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