Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

$k$ : 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 $G:\mathcal{C}\rightarrow (Sets)$?

share|improve this question
1  
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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.