fullyFaithfulForget₂ToMonCat — Mathlib

English

The forgetful functor from GrpCat to MonCat is fully faithful; it induces bijections on Hom-sets.

Русский

Функтор забывания из GrpCat в MonCat полностью полно; он задаёт биекции между множествами мороморфизмов.

LaTeX

$$$ (\\mathrm{forget}_{\\mathrm GrpCat\\to MonCat}).\\mathrm{FullyFaithful}$$$

Lean4

/-- The forgetful functor from groups to monoids is fully faithful. -/
@[to_additive fullyFaihtfulForget₂ToAddMonCat /--
    The forgetful functor from additive groups to additive monoids is fully faithful. -/
    ]
def fullyFaithfulForget₂ToMonCat : (forget₂ GrpCat.{u} MonCat).FullyFaithful where preimage f := ofHom f.hom

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