essImageDistTriang — Mathlib

English

Let L be a localization; the distinguished triangles in the image essImageDistTriang(D) are exactly those triangles in D that come from distinguished triangles in C via L.

Русский

Пусть L — локализация; разностного треугольники в образе essImageDistTriang(D) — это ровно те треугольники в D, которые происходят из distinguished triangles в C через L.

LaTeX

$$$T \in L.essImageDistTriang \quad\text{iff}\quad \exists\; T'\in distTriang(C),\; T \cong L.mapTriangle.obj T'$$$

Lean4

/-- Given a functor `C ⥤ D` from a pretriangulated category, this is the set of
triangles in `D` that are in the essential image of distinguished triangles of `C`. -/
def essImageDistTriang : Set (Triangle D) := fun T =>
  ∃ (T' : Triangle C) (_ : T ≅ L.mapTriangle.obj T'), T' ∈ distTriang C

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