A Result of Krasner in Categorial Form

Alessandro Linzi ()
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Alessandro Linzi: Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia

Mathematics, 2023, vol. 11, issue 24, 1-15

Abstract: In 1957, M. Krasner described a complete valued field ( K , v ) as the inverse limit of a system of certain structures, called hyperfields, associated with ( K , v ) . We put this result in purely category-theoretic terms by translating it into a limit construction in certain slice categories of the category of valued hyperfields and their homomorphisms. We replace the original metric-dependent arguments employed by Krasner with a clean and elegant transition to certain slice categories.

Keywords: valuation; completion; field; hyperfield; category theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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