Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Seven Trees in One   Following a remark of Lawvere, we explicitly exhibit a particularly
elementary bijection between the set T of finite binary trees and the set T^7
of seven-tuples of such trees. "Particularly elementary" means that the
application of the bijection to a seven-tuple of trees involves case
distinctions only down to a fixed depth (namely four) in the given seven-tuple.
We clarify how this and similar bijections are related to the free commutative
semiring on one generator X subject to X=1+X^2. Finally, our main theorem is
that the existence of particularly elementary bijections can be deduced from
the provable existence, in intuitionistic type theory, of any bijections at
all.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat