University of Minnesota Combinatorics Seminar
Friday, March 4, 2011
3:35pm in 570 Vincent Hall



Sets with a category action

Peter Webb

Univ. of Minnesota


Abstract

Sets with a group action are considered fundamental objects of study, with applications throughout combinatorics, algebra, topology, number theory, and elsewhere. Regarding a group as a category with a single object we define the more general notion of an action of a category, in particular considering actions of posets. We explore some basic properties, giving a definition of the Burnside ring of a category which is different to other such definitions which appear in the literature. The Burnside ring turns out to have special properties among other, similarly defined, functors of a certain type.