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math.CT2026
From Torsors to Topoi: An Introduction with a View Toward -Protocols in Cryptography
Takao Inoué
This paper provides a preparatory introduction to sheaves and topoi, written as a conceptual continuation of the author's earlier introduction to torsors and as preparatory backgro…
math.CT2026
On the Category-Theoretic Independence of Meaning, Object, Name and Existence
Takao Inoué
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 parti…
math.CT2026
Grothendieck's Geometric Universes and A Sheaf-Theoretic Foundation of Information Network
Takao Inoué
This paper proposes an interpretation of Grothendieck's geometric universes as a foundational framework for \emph{information networks}. We argue that Grothendieck topologies, shea…