Foundations of (∞, 2) -category theory
Emily Riehl (Johns Hopkins University)
MSRI: Simons Auditorium
Work of Joyal, Lurie and many other contributors can be summarized by
saying that ordinary 1-category theory extends to (1; 1)-category theory: that is,
there exist homotopical/derived analogs of 1-categorical results. As \brave new algebra" grows in inuence, 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; 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 (1; 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 \(1; 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 -
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 rst two, but need not read either in