Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: For a few elements more: A survey of finite Rees index   This paper makes a comprehensive survey of results relating to finite Rees
index for semigroups. In particular, we survey of the state of knowledge on
whether various finiteness properties (such as finite generation, finite
presentability, automaticity, and hopficity) are inherited by finite Rees index
subsemigroups and extensions. We survey other properties that are invariant
under passing to finite Rees index subsemigroups and extensions, such as the
cofinality and number of ends. We prove some new results: inheritance of
word-hyperbolicity by finite Rees index subsemigroups, and inheritance of
(geometric) hyperbolicity by finite Rees index extensions and subsemigroups
within the class of monoids of finite geometric type. We also give some
improved counterexamples. All the results are summarized in a table.

22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess