Algebra/Topology seminar

Peter James (Universiteit Utrecht)

Title: Shuffles in simplicial categories and simplicial operads

Abstract: Shuffles of simplices play a key role in certain constructions on simplicial sets, in particular in taking products of representables. Moerdijk and Weiss use shuffles of trees in an analogous way when setting up their theory of dendroidal sets. Certain simplicial sets, and certain simplicial categories, are used in equivalent ways as models for infinity categories. Similarly, certain dendroidal sets and certain simplicial operads may be used as models for infinity operads. 

This talk will introduce two product-like constructions, one for simplicial categories and the other for simplicial operads, which make use of shuffles of simplices and trees respectively. These return new monoidal structures; the point of interest is in how these interact with the models described above. This is work in progress.