op_rightToLeft — Mathlib

English

Similarly, Epi(t.rightToLeft.app X) is equivalent to Epi(F.map(t.adj₂.counit.app X)).

Русский

Аналогично, эпиморфизм t.rightToLeft.app X эквивалентен эпиморфизму F.map(t.adj₂.counit.app X).

LaTeX

$$$\forall X,\; \operatorname{Epi}(t.rightToLeft.app X) \iff \operatorname{Epi}\big(F.map\big(t.adj_2.counit.app X\big)\big)$$$

Lean4

/-- For an adjoint triple `F ⊣ G ⊣ H` where `G` is fully faithful, the natural transformation
`F.op ⟶ H.op` obtained from the dual adjoint triple `H.op ⊣ G.op ⊣ F.op` is dual to the natural
transformation `H ⟶ F`. -/
@[simp]
theorem op_rightToLeft : t.op.rightToLeft = NatTrans.op t.rightToLeft :=
  by
  ext
  rw [rightToLeft_eq_units, rightToLeft_eq_counits]
  simp

Похожие утверждения