On the Witt vectors in the Lawvere quantale

TL;DR

This paper explores the structure of Witt vectors within the min-plus algebra of extended non-negative real numbers and examines categories enriched over this monoidal structure.

Contribution

It introduces the concept of Witt vectors in the context of Lawvere quantale and studies their categorical properties.

Findings

Witt vectors form a monoidal category in the min-plus algebra.

Enriched categories over this structure exhibit unique properties.

Potential applications in metric and domain theory.

Abstract

In this note, we investigate the Witt vectors in the min-plus algebra of extended non-negative real numbers, and consider categories enriched over them viewed as a monoidal category.