ext — Mathlib

English

Morphisms in PresheafedSpace are determined by their base map and the component map; hence extensionality holds.

Русский

Гомоморфизмы в PresheafedSpace определяются по базовой карте и компонентной карте; следовательно, расширение встречается.

LaTeX

$$$\operatorname{Ext}_{\mathrm{PresheafedSpace}}(X,Y) \text{ is determined by base and c}$$$

Lean4

@[ext (iff := false)]
theorem ext {X Y : PresheafedSpace C} (α β : Hom X Y) (w : α.base = β.base)
    (h : α.c ≫ whiskerRight (eqToHom (by rw [w])) _ = β.c) : α = β :=
  by
  rcases α with ⟨base, c⟩
  rcases β with ⟨base', c'⟩
  dsimp at w
  subst w
  dsimp at h
  erw [whiskerRight_id', comp_id] at h
  subst h
  rfl
    -- TODO including `injections` would make tidy work earlier.

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