forget_createsLimitsOfSize — Mathlib

English

The limit of a functor into CommGrpCat is equipped with a commutative group structure; the limit object is a CommGroup.

Русский

Предел диаграммы в CommGrpCat наделён структурой коммутативной группы; предел является CommGroup.

LaTeX

$$$ \text{CommGrpCat.limitCommGroup } F \; \text{ is a CommGroup} $$$

Lean4

/-- The forgetful functor from groups to types creates all limits.
-/
@[to_additive (relevant_arg := 100) /-- The forgetful functor from additive groups to types creates all limits. -/
    ]
noncomputable instance forget_createsLimitsOfSize : CreatesLimitsOfSize.{w, v} (forget GrpCat.{u}) where
  CreatesLimitsOfShape := inferInstance

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