Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the category of structure species   The purpose of the present paper is to make a mathematical study of the
differences and relations among possible structures inherent in an object, as
well as of the whole structure constituted by them (i.e., the structure of
structures), against the background of the structuralism by Claude
L\'{e}vi-Strauss and others. Our discussion focuses on Blanchard's categorical
reformulation of the notion of structure species introduced originally by
Bourbaki. The main result of the present paper asserts that a category can be
reconstructed, up to a certain slight indeterminacy, from the category of
structure species on it. This result is partially motivated by various
reconstruction theorems that have been shown in the context of anabelian
geometry.

35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin