6 papers
The Burnside ring of simple -sets
José Miguel Calderón León, Alberto G. Raggi-Cárdenas, Itzel Rosas +1
The Burnside ring of a finite category, introduced by Webb, generalizes the classical Burnside ring of a finite group. However, unlike the classical case, the Burnside ring of a fi…
Characterization of groupoid categories in terms of its category of -sets
J. Miguel Calderón, Alberto Gerardo Raggi-Cárdenas, Itzel Rosas +1
A -set is a functor from the category to the category of finite sets and functions. The category of -sets, $\mathcal{C} - \operatorname*{set…
Indecomposable factors of Fibered Burnside Rings
Benjamín García, Alberto G. Raggi-Cárdenas
In this paper, we describe the indecomposable factors of a fibered Burnside ring in terms of bases coming from the standard basis. We provide a further characterization of each fac…
The global representation fibered ring
J. Miguel Calderón, Alberto G. Raggi-Cárdenas
In this paper, we combine the concepts of the fibered Burnside ring and the character ring, viewing them as fibered biset functors, into what we call the global representation fibe…
On fibered Burnside rings, fiber change maps and cyclic fiber groups
Benjamín García, Alberto G. Raggi-Cárdenas
Fibered Burnside rings appear as Grothendieck rings of fibered permutation representations of a finite group, generalizing Burnside rings and monomial representation rings. Their s…
The additive completion of the biset category
Jesús Ibarra, Alberto G. Raggi-Cárdenas, Nadia Romero
Let be a commutative unital ring. We construct a category of fractions , where is a finite group and is a finite -set, and with morphisms given…