# functor of Artinian rings in Deformation theory

$k$ : algebraically closed field

$\mathcal{C}$: category of local Artinian $k$-algebras with residue field $k$

$\hat{\mathcal{C}}$: category of complete local $k$-algebras with residue field $k$

Can you give an example to show that not every covariant functor $F:\hat{\mathcal{C}}\rightarrow (Sets)$ is of the form $\hat{G}$ for some $G:\mathcal{C}\rightarrow (Sets)$?

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Maybe if you say what is $\hat G$ –  Fernando Muro Jun 19 '13 at 13:12
I assume there is a typo? Should this be: not every $F: \widehat{C}\to Sets$ is of the form $\widehat{G}$ for some $G: C\to Sets$? –  Matt Jun 19 '13 at 16:38
You may want to register an account, so that you don't create new IDs. –  S. Carnahan Jun 20 '13 at 4:55