5 papers
Relating Brauer categories, Koszul complexes, and graph complexes
Geoffrey Powell
The purpose of this paper is to investigate the relationship between hairy graph complexes associated to cyclic operads and their counterparts for operads (and, more generally, dio…
Operads, modules over walled Brauer categories, and Koszul complexes
Geoffrey Powell
We investigate certain complexes that are associated to an operad in -vector spaces, where is a field of characteristic . This exploits the study of modules…
Filtering the linearization of the category of surjections
Geoffrey Powell
A filtration of the morphisms of the -linearization of the category of finite sets and surjections is constructed using a natural $k \mathbf{FI}^{o…
Functors on the category of finite sets revisited
Geoffrey Powell
We study the structure of the category of representations of , the category of finite sets and all maps, mostly working over a field of characteristic zero. This categ…
On the Passi and the Mal'cev functors
Geoffrey Powell
The author has shown that the category of analytic contravariant functors on , the category of finitely-generated free groups, is equivalent to the category of left mo…