2 citations · 4 across the 23 of their papers we have counts for
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Constructive Peter--Weyl Theory: What Is Known and What Remains Open
Takao Inoué
What is known about constructive Peter-Weyl theory, and what remains open? This expository article separates established theorems, comparisons between formulations, and questions r…
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…
Celebrating the Day of : Joyful Variations on Euler's Identity
Takao Inoué
This short essay celebrates the mathematical meaning of Pi Day through Euler's formula \[ e^{ix}=\cos x+i\sin x, \] from which Euler's identity \[ e^{iπ}+1=0 \] follows immediately…
An Introduction to Torsors in Mathematics with a View Toward -Protocols in Cryptography
Takao Inoué
This paper provides a preparatory introduction to torsors, written with a view toward later applications in the author's work. Rather than aiming at a comprehensive survey, the exp…
Modular Cocycles and Haar-Type Measures on Topological Loops
Takao Inoué
This paper is a continuation of the author's companion work \cite{InoueQuasi} on Haar-type measures for topological quasigroups, where the quasigroup setting was analyzed in connec…
Haar-Type Measures on Topological Quasigroups and Kunen's Theorem
Takao Inoué
Haar measure is a fundamental structure in harmonic analysis on locally compact groups. Its existence reflects the compatibility between topology and the associative algebraic stru…
Mayer--Vietoris and Twisted Čech Spectral Sequences for C-Algebras with Free Quantum Group Coefficients
Takao Inoué
We formulate a Mayer--Vietoris/Čech viewpoint on -theory for crossed products by discrete quantum groups, emphasizing how local-to-global gluing data interacts with quantum-grou…
Chirality and Racemization on Isotopy Classes of Loops: A Groupoid-Based Structural Theory
Takao Inoué
We develop a theory of chirality and racemization on isotopy classes of finite loops, formulated intrinsically within the loop isotopy groupoid understood in the categorical sense.…
A Formal Group Perspective on the Riemann Zeta Function
Takao Inoué
We develop a formal group--theoretic framework for the Riemann zeta function by treating its Euler product as an element of the multiplicative formal group …
Chirality and Racemization on Isotopy Classes of Quasigroups
Takao Inoué
We develop a structural and dynamical theory of chirality for quasigroups formulated at the level of isotopy classes. Interpreting isotopy as a gauge symmetry of re-coordinatizatio…
A Structural Fixed-Point Principle in Kunen's Theorem on Quasigroups
Takao Inoué
Kunen proved that a quasigroup satisfying a Moufang-type identity () must be a loop. We reformulate the argument in the category as a fixed-point extraction prin…
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…
Grothendieck Topologies and Sheaf-Theoretic Foundations of Cryptographic Security: Attacker Models and -Protocols as the First Step
Takao Inoué
Cryptographic security is traditionally formulated using game-based or simulation-based definitions. In this paper, we propose a structural reformulation of cryptographic security…
TAPO-Structured Description Logic for Information Behavior: Procedural and Oracle-Based Extensions
Takao Inoué
We introduce \emph{TAPO-Structured Description Logic} (TAPO--DL), a formal extension of classical description logic designed to model \emph{information behavior} as a structured, d…
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…
On Brain as a Mathematical Manifold: Neural Manifolds, Sheaf Semantics, and Leibnizian Harmony
Takao Inoué
We present a mathematical and philosophical framework in which brain function is modeled using sheaf theory over neural state spaces. Local neural or cognitive functions are repres…