# Mathematical Sciences Research Institute

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# Models for homotopical higher categories

## Introductory Workshop: Algebraic Topology January 27, 2014 - January 31, 2014

January 28, 2014 (03:30 PM PST - 04:30 PM PST)
Speaker(s): Julie Bergner (University of California)
Location: MSRI: Simons Auditorium
Video
Abstract

Models for homotopical categories, known as $(\infty,1)$-categories, are now fairly well-developed. Comparisons are in place between them, and there is a wide variety of applications ranging from topology to algebra to algebraic geometry. Generalizing them to models for homotopical higher categories, or $(\infty,n)$-categories, requires substantially greater technicality. Much work has been done in this direction, due to recent work of many authors, but the full picture is still very much work in progress. In this talk we will review different models for $(\infty,1)$-categories and discuss the number of ways they are being generalized to models for $(\infty,n)$-categories, as well as the known and conjectured comparisons between them

Supplements