Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on iterations of the $\mathbb A^1$-chain connected components
  construction   We show that the sheaf of $\mathbb A^1$-connected components of a Nisnevich
sheaf of sets and its universal $\mathbb A^1$-invariant quotient (obtained by
iterating the $\mathbb A^1$-chain connected components construction and taking
the direct limit) agree on field-valued points. This establishes an explicit
formula for the field-valued points of the sheaf of $\mathbb A^1$-connected
components of any space. Given any natural number $n$, we construct an $\mathbb
A^1$-connected space on which the iterations of the naive $\mathbb
A^1$-connected components construction do not stabilize before the $n$th stage.

18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys