2 citations · 4 across the 23 of their papers we have counts for
23 papers
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…
Epistemic systems and Flagg and Friedman's translation
Takao Inoué
In 1986, Flagg and Friedman \cite{ff} gave an elegant alternative proof of the faithfulness of Gödel (or Rasiowa-Sikorski) translation of Heyting arithmetic …
On humanization of mathematics: aesthetic mathematics
Takao Inoué
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches…
Axiomatic Rejection for the Propositional Fragment of Leśniewski's Ontology
Takao Inoué, Arata Ishimoto, Mitsunori Kobayashi
A Hilbert-type axiomatic rejection for the propositional fragment of Leśniewski's ontology is proposed. Also a Gentzen-type axiomatic rejection $\math…
How to Make a New Logic
Takao Inoué
We discuss about how to make a new logic with considering a slogan: \it take the inversion of what you know. \rm Suppose that we have a Gentzen-style logical system . The operat…
The consistency of arithmetic from a point of view of constructive tableau method with strong negation, Part I: the system without complete induction
Takao Inoué
In this Part I, we shall prove the consistency of arithmetic without complete induction from a point of view of strong negation, using its embedding to the tableau system …
On Bergman's Diamond Lemma for Ring Theory
Takao Inoué
This expository and review paper deals with the Diamond Lemma for ring theory, which is proved in the first section of G. M. Bergman, The Diamond Lemma for Ring Theory, Advances in…
On Blass translation for Leśniewski's propositional ontology and modal logics
Takao Inoué
In this paper, we shall give another proof of the faithfulness of Blass translation (for short, -translation) of the propositional fragment of Leśniewski's ontology in…