Videos

Models for homotopical higher categories

Presenter
January 28, 2014
Keywords:
  • infinity-categories
  • (infinity, n)-categories
  • cobordism theory
  • cobordism category
  • Segal spaces
  • Theta construction
  • Theta_n spaces
MSC:
  • 18-XX
  • 18Dxx
  • 18D50
  • 18D99
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.
Supplementary Materials