ModuleCat.hasLimitsOfSize

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

This theorem states that for any type `R` that is a Ring, the category of `R`-modules has limits of all sizes. In mathematical terms, given any ring `R`, the category formed by its modules and their morphisms has all possible limits. This is a fundamental property of the category of modules over a ring in category theory, and it asserts the existence of products, equalizers, and more generally limits for any diagram in this category.

More concisely: For any ring `R`, the category of `R`-modules has all limits.