ext_of_isTriangulatedClosed₁ — Mathlib

English

The entire construction of rotate and invRotate yields an equivalence between the category of triangles and itself, with rotCompInvRot and invRotCompRot providing the unit and counit isomorphisms.

Русский

Вся конструкция rotate и invRotate образует эквивалентность между категорией треугольников и самой собой; rotCompInvRot и invRotCompRot служат единицами и коунинами изоморфизмов.

LaTeX

$$$\\text{triangleRotation} : \\mathbf{Triangle}(C) \\simeq \\mathbf{Triangle}(C)$ with unit/ counit given by rotCompInvRot and invRotCompRot.$$

Lean4

theorem ext_of_isTriangulatedClosed₁ [P.IsTriangulatedClosed₁] [P.IsClosedUnderIsomorphisms] (T : Triangle C)
    (hT : T ∈ distTriang C) (h₂ : P T.obj₂) (h₃ : P T.obj₃) : P T.obj₁ := by
  simpa only [isoClosure_eq_self] using P.ext_of_isTriangulatedClosed₁' T hT h₂ h₃

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