2015/02/17 by Nakaoka, Hiroyuki
#Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1502.04821
In the previous article 'A Mackey-functor theoretic interpretation of biset functors', we have constructed the 2-category \mathbbS of finite sets with variable finite group actions, in which bicoproducts and bipullbacks exist. As shown in it, biset functors can be regarded as a special class of Mackey functors on \mathbbS. In this article, we equip \mathbbS with a system of adjoint triplets, which satisfies properties analogous to a derivator. This system encodes the six operations for finite groups. As a corollary, we show that the associated Burnside rings satify analogous properties to a Tambara functor, in the context of biset functor theory.