17 papers
Constructive Peter--Weyl Theory: What is Known and What Remains Open
Takao Inoué
This survey-style note reviews constructive versions of the Peter--Weyl theorem in the Bishop--Coquand--Spitters line. Its main purpose is to clarify which parts of the classical P…
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 \[ e^{iÏ}+1=0 \] follows immediatel…
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…