On the Category-Theoretic Independence of Meaning, Object, Name and Existence
Abstract
We prove a category-theoretic independence theorem for four fundamental notions: meaning, object, name, and existence. Working in a Lawvere-style categorical semantics and in particular in toposes, we show that these notions occupy distinct structural levels (object, morphism, element, and internal logical level) and are not uniformly recoverable from one another. The key separation arises between internal existence and global naming. Using a concrete example in the topos -the sheaf of local sections of a nontrivial covering-we exhibit an object that is internally inhabited but admits no global element. These results provide a precise structural basis for treating geometric universes as foundational frameworks for information networks.
Keywords
Cite
@article{arxiv.2602.18033,
title = {On the Category-Theoretic Independence of Meaning, Object, Name and Existence},
author = {Takao Inoué},
journal= {arXiv preprint arXiv:2602.18033},
year = {2026}
}
Comments
14 pages. Includes a category-theoretic independence theorem for the notions of meaning, object, name, and existence, together with a concrete example in the topos $\mathbf{Sh}(S^1)$. An informal guide with a schematic figure is included