hasLimit — Mathlib

English

For a functor F : J ⥤ CommGrpCat, the limit cone is given by a chosen limit cone structure, possibly after an adjustment to Small objects.

Русский

Для F : J ⥤ CommGrpCat предел задаётся выбранной структурой предел-конуса; возможно, с небольшими преобразованиями.

LaTeX

$$$ \text{limitCone } F = \text{Cone}(F) \text{ (with chosen universal cone)}$$$

Lean4

/-- If `(F ⋙ forget CommGrpCat).sections` is `u`-small, `F` has a limit. -/
@[to_additive /-- If `(F ⋙ forget AddCommGrpCat).sections` is `u`-small, `F` has a limit. -/
    ]
instance hasLimit : HasLimit F :=
  HasLimit.mk
    { cone := limitCone F
      isLimit := limitConeIsLimit F }

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