AlgebraCat.hasLimitsOfSize

theorem AlgebraCat.hasLimitsOfSize : ∀ {R : Type u} [inst : CommRing R] [inst_1 : UnivLE.{v, w}], CategoryTheory.Limits.HasLimitsOfSize.{t, v, w, max (w + 1) u} (AlgebraCat R)

This theorem states that for any given commutative ring `R`, the category of `R`-algebras has all limits of any size. In other words, for any diagram in the category of `R`-algebras, there exists a limit object in the category that serves as a universal cone for the diagram. This universal property is a key characteristic in category theory and this theorem ensures it holds for the category of `R`-algebras.

More concisely: The category of commutative rings `R` and their `R`-algebras has all limits.