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Mackey functors from the viewpoint of double category theories

Mawei Wu

Abstract

Let $G$ be a finite group. In this paper, we first introduce a new notion, so-called the Mackey double category of $G$. Then we prove that the category of Mackey double categories and the category of Mackey functors of $G$ are equivalent.

Mackey functors from the viewpoint of double category theories

Abstract

Let be a finite group. In this paper, we first introduce a new notion, so-called the Mackey double category of . Then we prove that the category of Mackey double categories and the category of Mackey functors of are equivalent.

Paper Structure

This paper contains 7 sections, 1 theorem, 17 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Mackey functors
  4. Double category theories
  5. Reformulate Mackey functors via double categories
  6. Mackey double categories
  7. Equivalence between Mackey functors and Mackey double categories

Key Result

Theorem 3.2.1

Let $G$ be a finite group, then the category of Mackey functors and the category of Mackey double categories are equivalent, that is

Theorems & Definitions (10)

  • Definition 2.1.1
  • Definition 2.2.1
  • Definition 2.2.2
  • Definition 3.1.1
  • Remark 3.1.2
  • Definition 3.1.3
  • Definition 3.1.4
  • Theorem 3.2.1
  • proof
  • Remark 3.2.2