Real Mathematics Diagram

Lemma 3.9. Consider a diagram x₀ → x₁ → x₂ → ⋯ in a stable ∞-category. Suppose that each αₙ admits a factorisation αₙ: xₙ → x′ₙ → x″ₙ → xₙ₊₁ where ϕₙ and ψₙ are equivalences. Then colimₙ xₙ is equivalent to the cofiber of the endomorphism of the map ⊕ₙ∈ℕ xₙ ⊕ x″ₙ → ⊕ₙ∈ℕ xₙ ⊕ x′ₙ represented by the following diagram: x₀ ⊕ x″₀ ⊕ x₁ ⊕ x″₁ ⊕ x₂ ⊕ x″₂ ⊕ ⋯ ↓id ↘−ϕ₀ ↓ψ₀⁻¹ ↘−β₀ ↓id ↘−ϕ₁ ↓ψ₁⁻¹ ↘−β₁ ↓id ↘−ϕ₂ ↓ψ₂⁻¹ ↘−β₂ ↘⋯ x₀ ⊕ x′₀ ⊕ x₁ ⊕ x′₁ ⊕ x₂ ⊕ x′₂ ⊕ ⋯

A dense mathematical lemma presents a diagram in a stable infinity-category, with objects connected by arrows, equivalences, and coproduct notation. The joke is that the uploader presents genuinely intimidating higher mathematics as “real mathematics,” making it a reaction image for complicated formulas, academic overconfidence, or situations nobody understands. EN: A dense mathematical lemma presents a diagram in a stable infinity-category, with objects connected by arrows, equivalences, and coproduct notation. The joke is that the uploader presents genuinely intimidating higher mathematics as “real mathematics,” making it a reaction image for complicated formulas, academic overconfidence, or situations nobody understands.

• @pokupkabitka / 30716 2023-11-09