counit_epi_of_R_faithful — Mathlib

English

If the right adjoint R is faithful, then each component of the counit is epic.

Русский

Если правый аплад R надёжный, тогда каждый компонент контудиан (counit) эпиморфен.

LaTeX

$$∀ X, Epi (h.counit.app X) when R is faithful$$

Lean4

/-- If the right adjoint is faithful, then each component of the counit is an epimorphism. -/
instance counit_epi_of_R_faithful [R.Faithful] (X : D) : Epi (h.counit.app X) where
  left_cancellation {Y} f g hfg := R.map_injective <| (h.homEquiv (R.obj X) Y).symm.injective <| by simpa using hfg

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