# Does the category of graded rings have limits?

Let $\mathfrak{C}$ be the category of ($\mathbb{Z}$)-graded-commutative rings. Does this category have limits in it?

I am particulary interested in power series rings over a field. Is there a reasonable way to view such a ring as a graded ring?

Let $R = k[x]$ be a graded ring. Let $I=(x)$ be a graded ideal. Is $\varprojlim R/I^n$ an element of $\mathfrak{C}$?

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Since this category has product and equalizers, it has limits. –  Yang Zhou Jul 28 '12 at 2:05

The limit you wrote down is isomorphic in the category of rings to the ring of power series over $k$. A grading is a decomposition into direct sums. But power series have infinitely many terms...This is a kind of vague explanation for why I think it isn't possible.