Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On integral schemes over symmetric monoidal categories   We propose notions of "Noetherian" and "integral" for schemes over an abelian
symmetric monoidal category $(\mathcal C,\otimes,1)$. For Noetherian integral
schemes, we construct a "function field" that is a commutative monoid object of
$(\mathcal C,\otimes,1)$. Under certain conditions, we show that a Noetherian
scheme over $(\mathcal C,\otimes,1)$ is integral if and only if it is reduced
and irreducible.

29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th