Two comparison theorems for semiring schemes

TL;DR

This paper compares two frameworks for semiring schemes, showing they are equivalent and that the topological space can be reconstructed from the functor of points.

Contribution

It establishes the canonical equivalence between the topological space approach and the functor of points approach for semiring schemes.

Findings

The topological space can be recovered from the functor of points.

The two notions of semiring schemes are canonically equivalent as categories.

Abstract

In this note, we compare the two approaches to semiring schemes as topological spaces with a structure sheaf and as a functor of points. We explain and prove the following two results: (1) the topological space can be recovered from the functor of points; (2) the two notions of semiring schemes are canonically equivalent as categories.