Note on the conflation of relabeling with opposite
This note isolates a small ambiguity that occurs when one moves between covariant and contravariant functors i … 続きを読む
Mathematics
Note on Sierpiński Classifier
Elementary note. A Sierpiński space is introduced along with its representability of the open-set functor , th … 続きを読む
Meaning of (n,r)-Category
A useful notation with unstable boundaries The notation (n,r)-category is meant to classify higher categories … 続きを読む
ε-δの先 — 論理が概念を内包しないケース
ε-δ論法について 「ε-δ論法」というのは、数学科に入ったばかりの1年生にとって、ちょっとした通過儀礼のような存在のようである。入学してほどなくして、講義でいきなり といった、見慣れない論理 … 続きを読む
Asymptote installation and setup 2026 (Windows)
0. Overview This is the installation and configuration steps of Asymptote, which is tailored to a specific res … 続きを読む
Memo in a reduction strategy of a map
This is my random thought on how we should investigate the properties of a map in general. The mapping path sp … 続きを読む
数学で生きること─AI時代における知性
序章 2026年現在、私たちはAIとともに数学を語り、発見する時代に生きている。かつて数学の発見は、時間をかけ、専門文献を読み、問題の輪郭をゆっくりと捉える営みだった。未知の理論に触れ、数年に及ぶ忍耐と直感の積み重ねを経 … 続きを読む
The multi-filtration and the multi-persistence on a total object
Discussion and Verdict I have observed a tendency to conflate, or at least structurally identify, (multi-) fil … 続きを読む
The Fractions
Fractions are deceptively difficult. I have seen many parents agonize over how to explain concepts like 1/4 or … 続きを読む
Sheafification as a free construction
In the world of algebra, we often encounter “free” constructions. Think of the free group or the p … 続きを読む