Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A correction to the uniqueness of a partial perfect locality over a
  Frobenius P-category   Let $p$ be a prime, $P$ a finite p-group and $\cal F$ a Frobenius
$P$-category. In "Existence, uniqueness and functoriality of the perfect
locality over a Frobenius $P$-category", Algebra Colloquium, 23(2016) 541-622,
we also claimed the uniqueness of the partial perfect locality $\cal L^{\frak
X}$ over any up-closed set $\frak X$ of $\cal F$-selfcentralizing subgroups of
$P$, but recently Bob Oliver exhibit some counter-examples, demanding some
revision of our arguments. In this Note we show that, up to replacing the
perfect localities by the "extendable" perfect localities over any up-closed
set $\frak X$ of $\cal F$-selfcentralizing subgroups of $P$, our arguments are
correct, still proving the existence and the uniqueness of the perfect $\cal
F^{\rm sc}$-locality, since it is "extendable". We take advantage to simplify
some of our arguments.

27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex