IsCodetecting — Mathlib

English

If h is a codetecting family and α is an equivalence, then the image α.functor.obj '' 𝒢 is codetecting.

Русский

Если 𝒢 кодетагощее и α — эквивалентность, то образ 𝒢 под α кодетагощее.

LaTeX

$$$IsCodetecting(\alpha.functor.obj '' 𝒢)$$$

Lean4

/-- We say that `𝒢` is a codetecting set if the functors `C(-, G)` collectively reflect
    isomorphisms, i.e., if any `h` with codomain in `G` uniquely factors through `f`, then `f` is
    an isomorphism. -/
def IsCodetecting (𝒢 : Set C) : Prop :=
  ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ G ∈ 𝒢, ∀ (h : X ⟶ G), ∃! h' : Y ⟶ G, f ≫ h' = h) → IsIso f

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