Foundations of (∞, 2) category theory
Women in Topology November 29, 2017  December 01, 2017
Location: MSRI: Simons Auditorium
higher category theory
homotopy theory
model categories
4Riehl
Work of Joyal, Lurie and many other contributors can be summarized by saying that ordinary 1category theory extends to (∞,1)category theory: that is, there exist homotopical/derived analogs of 1categorical results. As “brave new algebra” grows in influence, many areas of mathematics now require homotopical/derived analogs of 2categorical 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 quasicategorical 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 2category 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 2categorical limits”, Bull. Austral. Math. Soc., Vol. 39 (1989), pp. 301317.
Potential participants should skim bits of the first two, but need not read either in full.
Riehl Notes

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