On the category of structure species

Abstract: 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.