map_restrictFullyFaithful_unit_app

English

Under a restriction of a fully faithful adjunction, the counit on X is given by inv components and the adjunction counit.

Русский

При ограничении на полностью достоверную пары сопряжений, коуницийная на X задаётся через инверсии и коуницию.

LaTeX

$$$(iD.map ((adj.restrictFullyFaithful hiC hiD comm1 comm2).counit.app X)) = comm1.inv.app (R.obj X) \\; \\circ \\; L'.map (comm2.inv.app X) \\; \\circ \\; adj.counit.app (iD.obj X)$$$

Lean4

@[simp, reassoc]
theorem map_restrictFullyFaithful_unit_app (X : C) :
    iC.map ((adj.restrictFullyFaithful hiC hiD comm1 comm2).unit.app X) =
      adj.unit.app (iC.obj X) ≫ R'.map (comm1.hom.app X) ≫ comm2.hom.app (L.obj X) :=
  by simp [restrictFullyFaithful]

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