fullyFaithful — Mathlib

English

The truncated skeleton functor is faithful: it reflects distinct morphisms, under suitable pointwise Kan extension assumptions.

Русский

Усечённый скелетон-функтор верен: он отражает различия морфизмов при подходящих условиях Кан-расширения.

LaTeX

$$$$ \\mathrm{Sk}.\\mathrm{Faithful} $$$$

Lean4

/-- Since `Truncated.inclusion` is fully faithful, so is right Kan extension along it. -/
noncomputable def fullyFaithful : (Truncated.cosk (C := C) n).FullyFaithful := by
  apply Adjunction.fullyFaithfulROfIsIsoCounit (coskAdj n)

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