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The lower plus and upper plus constructions for fibered biset functors

J. Miguel Calderón

Abstract

Let A be an abelian group, not necessarily finite. The main objective of this paper is to provide two constructions for a fibered A-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 {.}.

The lower plus and upper plus constructions for fibered biset functors

Abstract

Let A be an abelian group, not necessarily finite. The main objective of this paper is to provide two constructions for a fibered A-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 {.}.
Paper Structure (15 sections, 20 theorems, 179 equations)

This paper contains 15 sections, 20 theorems, 179 equations.

Table of Contents

  1. Introduction
  2. Fibered bisets
  3. The lower plus and upper plus constructions on subcategories $\mathcal{D}$ of $\mathcal{C}$
  4. The functor lower plus for $A$-fibered bisets
  5. The functor $\Gamma_{F}(U): \Gamma_{F}(G) \longrightarrow \Gamma_{F}(H)$.
  6. Multiplicative Structure of $F_+$
  7. The functor upper plus for $A$-fibered bisets
  8. Multiplicative Structure of $F^+(G)$
  9. The mark morphism
  10. Green Functors
  11. example
  12. The Functor $\mathbb{K}R_\mathbb{C}$
  13. The global representation fibered ring functor
  14. The functor $R^{ \mathbb{C}^\times}_{\mathbb{C},+}$
  15. Adjunciones

Key Result

Theorem 2.1

For $(U, \varphi)\in \mathcal{M}(G \times H)$ and $(V, \psi) \in \mathcal{M}(H \times K)$ one has where $H_t = k_2(U) \cap ^tk_1(V)$.

Theorems & Definitions (57)

  • Theorem 2.1: Corollary 2.5 of fibered
  • Theorem 2.2: Proposition 2.8 of fibered
  • Lemma 2.3
  • Definition 3.1
  • Remark 3.2
  • proof
  • Definition 3.3
  • Definition 3.4
  • Remark 3.5
  • Proposition 3.6
  • ...and 47 more