Group completion in the K-theory and Grothendieck-Witt theory of proto-exact 
categories

Eberhardt, Jens Niklas; Lorscheid, Oliver; Young, Matthew B.

doi:10.1016/j.jpaa.2022.107018

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Group completion in the K-theory and Grothendieck-Witt theory of proto-exact categories

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Eberhardt, Jens Niklas
Max Planck Institute for Mathematics, Max Planck Society;

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Lorscheid, Oliver
Max Planck Institute for Mathematics, Max Planck Society;

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Young, Matthew B.
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1016/j.jpaa.2022.107018
(Publisher version)

https://doi.org/10.48550/arXiv.2009.12635
(Preprint)

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Eberhardt-Lorscheid-Young_Group completion in the K-theory and Grothendieck-Witt theory of proto-exact categories_2022.pdf
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Citation

Eberhardt, J. N., Lorscheid, O., & Young, M. B. (2022). Group completion in the K-theory and Grothendieck-Witt theory of proto-exact categories. Journal of Pure and Applied Algebra, 226(8): 107018. doi:10.1016/j.jpaa.2022.107018.

Cite as: https://hdl.handle.net/21.11116/0000-0009-F99B-0

Abstract

We study the algebraic $K$-theory and Grothendieck-Witt theory of proto-exact
categories, with a particular focus on classes of examples of
$\mathbb{F}_1$-linear nature. Our main results are analogues of theorems of
Quillen and Schlichting, relating the $K$-theory or Grothendieck-Witt theories
of proto-exact categories defined using the (hermitian) $Q$-construction and
group completion.