Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A coordinate-free definition of Hurwitz spaces   Given a couple of subspaces $\mathcal{Y}\subset\mathcal{X}$ of the complex
plane $\mathbb{C}$ satisfying some mild conditions (nice couple), and given a
PMQ-pair $(\mathcal{Q},G)$, consisting of a partially multiplicative quandle
(PMQ) $\mathcal{Q}$ and a group $G$, we introduce a Hurwitz space
$\mathrm{Hur}(\mathcal{X},\mathcal{Y};\mathcal{Q},G)$, containing
configurations of points in $\mathcal{X}\setminus\mathcal{Y}$ and in
$\mathcal{Y}$ with monodromies in $\mathcal{Q}$ and in $G$, respectively. The
construction generalises classical Hurwitz spaces of points in the plane
$\mathbb{C}$ with monodromies in a group $G$. We introduce a notion of
morphisms between nice couples of subspaces of the plane, and prove that
generalised Hurwitz spaces are functorial both in the nice couple and in the
PMQ-group pair. For a locally finite PMQ $\mathcal{Q}$ we prove a homeomorphism
between $\mathrm{Hur}((0,1)^2;\mathcal{Q}_+)$ and the simplicial Hurwitz space
$\mathrm{Hur}^{\Delta}(\mathcal{Q})$, introduced in previous work of the
author: this provides in particular $\mathrm{Hur}((0,1)^2;\mathcal{Q}_+)$ with
a cell stratification in the spirit of Fox-Neuwirth and Fuchs.

18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an