A rigorous categorical formulation of Δ‑ontology is proposed — an approach to the foundations of mathematics in which the first principle is not a structureless point, but infinity ℑ = △₁,₁ (an isosceles right triangle with legs 1 and hypotenuse √2). It is shown that the fundamental contradictions of mathematics and physics — singularities, the conflict between quantum mechanics and relativity, “heat death” — are rooted in the concept of a point. Replacing the point with infinity turns entropy from a measure of chaos into a measure of the striving for equilibrium; the concept of intropy is introduced as a quantity that decreases when approaching harmony and energy economy. A categorical framework is constructed: the category of distinctions Rel with orthogonality morphisms, universal closure as a pullback, elementary relational triples, self‑similarity in the form of an equivalence of slice categories, measure as an enriched functor, limit relational complexes as direct limits, and function spaces as inverse limits of presheaves. It is proved that the spectral gap of the natural Laplacian equals λ₁ = 1 − ½√2. Categorical versions of the Poincaré conjecture and the Yang–Mills mass gap problem are formulated. A logical interpretation is given: infinity acts as a forcing code, and mathematics appears as a family of Δ‑mosaics.
Alexey (KAMAZ) Petrov (Sun,) studied this question.