lift_comp_inv_left — Mathlib

English

Symmetrically, lift (ι ≫ f) applied to f and composed with μ yields the unit-counit relation: toUnit ∘ η.

Русский

Симметрично, lift (ι ≫ f) применяется к f и затем следует μ; результат равен toUnit ∘ η.

LaTeX

$$$\mathrm{lift}(\iota \circ f, f) \circ \mu = \mathrm{toUnit} \circ \eta$$$

Lean4

@[reassoc (attr := simp)]
theorem lift_comp_inv_left [GrpObj B] (f : A ⟶ B) : lift (f ≫ ι) f ≫ μ = toUnit _ ≫ η :=
  by
  have := f ≫= left_inv B
  rwa [comp_lift_assoc, comp_id, reassoc_of% toUnit_unique (f ≫ toUnit B) (toUnit A)] at this

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