An equivalence between two frameworks for real algebraic K-theory

TL;DR

This paper establishes an equivalence between two frameworks for real algebraic K-theory, connecting the approaches of Calmès et al. and the authors for different categorical settings.

Contribution

It demonstrates a formal equivalence between the real K-theory spectra in two different categorical frameworks, unifying their perspectives.

Findings

Proves an equivalence between the real K-theory spectra of two frameworks.

Bridges the approaches of Calmès et al. and the authors' work.

Enhances understanding of real algebraic K-theory in different categorical contexts.

Abstract

We prove an equivalence between the real $K$-theory genuine $C_2$-spectra of Calm\`es et al. for Poincar\'e $\infty$-categories and the one of the authors of this work for Waldhausen $\infty$-categories with genuine duality.