coeq₃_condition₁ — Mathlib

English

For morphisms f, g, h: j1 → j2, the morphism coeq₃Hom(f,g,h) coequalizes f and g, i.e., f ≫ coeq₃Hom(f,g,h) = g ≫ coeq₃Hom(f,g,h).

Русский

Для стрелок f, g, h: j1 → j2, morphism coeq₃Hom(f,g,h) кофаилирует f и g, то есть f ≫ coeq₃Hom(f,g,h) = g ≫ coeq₃Hom(f,g,h).

LaTeX

$$$\\forall {C} [\\text{Category } C] [\\text{IsFilteredOrEmpty } C] \\{j_1 j_2 : C\\} (f g h: j_1 \\to j_2), \\\\ f \\\\Rightarrow g \\\\Rightarrow f \\\\circ coeq₃Hom(f,g,h) = g \\\\circ coeq₃Hom(f,g,h).$$$

Lean4

theorem coeq₃_condition₁ {j₁ j₂ : C} (f g h : j₁ ⟶ j₂) : f ≫ coeq₃Hom f g h = g ≫ coeq₃Hom f g h := by
  simp only [coeq₃Hom, ← Category.assoc, coeq_condition f g]

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