The lower plus and upper plus constructions for fibered biset functors
Year: 2025
Type: article
Abstract: Let A be an abelian group, not necessarily finite. The main objective of this paper is to provide two constructions for an A-fibered biset functor. The first is the lower plus construction, and the other is the upper plus construction. These constructions coincide with the lower plus and upper plus constructions for biset functors (see [2]) when the fiber is the trivial group $$\lbrace \cdot \rbrace $$ { · } . To generate these constructions, it is necessary to have a family $$\mathcal {G}$$ G of finite groups and a function $$\mathcal {S}$$ S such that, for all $$G, H \in \mathcal {G}$$ G , H ∈ G , we relate them to a subset $$\mathcal {S}(G, H)$$ S ( G , H ) of $$\mathcal {M}^A (G, H)= \mathcal {M}(G,H):=\lbrace (L,\varphi ) \mid L\le G\times H, \ \varphi \in \operatorname {Hom}(L,A)\rbrace $$ M A ( G , H ) = M ( G , H ) : = { ( L , φ ) ∣ L ≤ G × H , φ ∈ Hom ( L , A ) } The pair $$\mathcal {(G,S)}$$ ( G , S ) satisfies certain axioms outlined in Definition 3.1. These axioms are essential for enabling the pair $$\mathcal {(G, S)}$$ ( G , S ) to generate the subcategory $$\mathcal {D}$$ D of the category of A-fibered bisets, denoted as $$\mathcal {C}^A.$$ C A . . In Sect. 2, we recall and extend the basic definitions and results for fibered bisets and fibered biset functors. In Sect. 3, the upper and lower constructions are defined. For this purpose, the pair $$\mathcal {(G, S)}$$ ( G , S ) is associated with $$\mathcal {(G, S_+ )}$$ ( G , S + ) and $$\mathcal {(G, S^+ )}$$ ( G , S + ) , with which we can construct the subcategories $$\mathcal {D}_+$$
Author: J. Miguel Calderón
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Award: G1530468784
OpenAlex ID: W4408891145