η_ε_app — Mathlib

English

Similarly, the η and ε components compose to the identity in the opposite order: (η F).app X ; (ε F).app X = id.

Русский

similarly, η и ε композиция идёт в тождественный морфизм: (η F).app X ; (ε F).app X = id.

LaTeX

$$$ (\\eta F).app X \\circ (\\varepsilon F).app X = \\mathrm{id}_X$$$

Lean4

@[reassoc (attr := simp)]
theorem η_ε_app (X : C) [F.Monoidal] : (η F).app X ≫ (ε F).app X = 𝟙 _ :=
  (εIso F).inv_hom_id_app X

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