University of Sydney Algebra Seminar

Daniel Stevenson (University of Adelaide)

Friday 27 September, 12-1pm, Place: Carslaw 375

A classical theorem for simplicial sets, revisited

Simplicial sets became popular in the 1950s as a combinatorial way to study the homotopy theory of topological spaces. They are more robust than the older notion of simplicial complexes, which were introduced for the same purpose. In this talk, we will review some classical functors arising in the theory of simplicial sets, some well-known, some not-so-well-known. In particular we will show how, by adopting a more categorical viewpoint, one may give a simple proof of an old theorem of Kan's relating the classifying space functor and the simplicial loop group functor.