Algebra/Topology Seminar

Speaker: Adam Dauser
Title: Unfolding monoidal (∞,n)-categories
Abstract:
E k-monoidal (∞, n)-categories C are a very complicated piece of data. One of the most subtle issues is the compatibility between horizontal and vertical composition. The basic idea of unfolding is that if every object of C has a (left and a right) dual, Hom(X, Y)=Hom(1, Y ⊗ X^) and C can be recovered from some kind of functor Hom(1, -) with values in (∞,n-1)Cat. Making this precise and iterating it allows a description of certain E k-monoidal (∞, n)-categories entirely in terms of (∞, 1)-categories, which are comparatively well developed.