Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric morphisms between toposes of monoid actions: factorization
  systems   Let M, N be monoids, and PSh(M), PSh(N) their respective categories of right
actions on sets. In this paper, we systematically investigate correspondences
between properties of geometric morphisms PSh(M) $\rightarrow$ PSh(N) and
properties of the semigroup homomorphisms M $\rightarrow$ N or
flat-left-N-right-M-sets inducing them. More specifically, we consider
properties of geometric morphisms featuring in factorization systems, namely:
surjections, inclusions, localic morphisms, hyperconnected morphisms,
terminal-connected morphisms, {\'e}tale morphisms, pure morphisms and complete
spreads. We end with an application to topos-theoretic Galois theory to the
special case of toposes of the form PSh(M).

16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org