pullback_functorPushforward_equivalence_eq

English

If F is full and faithful, then (R.arrows.functorPushforward F) (F.map f) is equivalent to R f for any f: Y ⟶ X.

Русский

Если F полно и тщательно сохраняет морфизмы, то (R.arrows.functorPushforward F) (F.map f) эквивалентно R f для любого f: Y ⟶ X.

LaTeX

$$$(R.arrows.functorPushforward F)(F.map f) \\leftrightarrow R f$$$

Lean4

theorem pullback_functorPushforward_equivalence_eq {X : C} (S : Sieve X) :
    Sieve.pullback (e.unit.app X) (Sieve.functorPushforward e.inverse (Sieve.functorPushforward e.functor S)) = S := by
  ext; simp

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