A result of Krasner in categorial form

TL;DR

This paper reformulates Krasner's 1957 result on complete valued fields using category theory, specifically through limit constructions in slice categories of valued hyperfields and their homomorphisms.

Contribution

It provides a purely categorical reformulation of Krasner's description of complete valued fields, connecting valuation theory with hyperfield limits.

Findings

Categorical reformulation of Krasner's theorem

Limit construction in slice categories of valued hyperfields

Enhanced understanding of valued field structures

Abstract

In 1957 M.\ Krasner described a complete valued field $(K,v)$ via the projective limit of a system of certain structures, called hyperfields, associated to $(K,v)$. We put this result in purely category-theoretic terms by translating into a limit construction in certain slice categories of the category of valued hyperfields and their homomorphisms.