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An equivalence between the real S- and the hermitian Q-construction

Hadrian Heine, Markus Spitzweck, Paula Verdugo

Abstract

We build a hermitian Q-construction that extends that of Calmès et al, and compare it with the real S-construction of the current authors. From this, we deduce an equivalence between the real K-theory genuine $C_2$-spaces of the aforementioned works.

An equivalence between the real S- and the hermitian Q-construction

Abstract

We build a hermitian Q-construction that extends that of Calmès et al, and compare it with the real S-construction of the current authors. From this, we deduce an equivalence between the real K-theory genuine -spaces of the aforementioned works.

Paper Structure

This paper contains 8 sections, 8 theorems, 18 equations.

Table of Contents

  1. Introduction
  2. Background
  3. Input
  4. The real $S_\bullet$-construction
  5. Real $K$-theory space
  6. Setting the stage
  7. $\infty$-categories with pro-duality
  8. $\infty$-categories with genuine pro-duality

Key Result

Theorem 1

Let ${\mathcal{C}}$ be a Waldhausen $\infty$-category with genuine duality. The map of simplicial exact $\infty$-categories with genuine duality is an equivalence.

Theorems & Definitions (34)

  • Theorem
  • Corollary
  • Definition 2.1
  • Remark 2.2
  • Definition 2.3
  • Definition 2.5
  • Definition 2.6
  • Remark 2.7
  • Definition 2.8
  • Definition 2.9
  • ...and 24 more