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• CommentRowNumber1.
• CommentAuthorTobyBartels
• CommentTimeOct 25th 2009

Todd started Schur functor. I added internal links and wrote linear category to be the target of one of them.

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeOct 25th 2009

Thanks, but I should say that I was in the middle of an edit when you did all that, and my submission erased your links, which I tried to reinsert. Please check: the link to "change of base" was supposed to point to an extant page, but I'm not sure which.

• CommentRowNumber3.
• CommentAuthorTobyBartels
• CommentTimeOct 25th 2009

Ah, your edit took longer than 30 minutes, so the lock timed out! And here I thought that you had cancelled it.

• CommentRowNumber4.
• CommentAuthorTodd_Trimble
• CommentTimeOct 25th 2009

Ah, I had no idea that locks time out! That's annoying, but at least now I know. I was busy trying to get the kids in bed and so on when it happened.

• CommentRowNumber5.
• CommentAuthorTobyBartels
• CommentTimeOct 25th 2009

I believe that they time out so that people can't lock a page forever if they just forget about it or their Internet connection crashes or something.

Sometimes I'll save a draft every 15 minutes or so to prevent it.

• CommentRowNumber6.
• CommentAuthorGuest
• CommentTimeOct 26th 2009
To get around the spam filter in the minimum time, I'll drop my intended comment for Schur functor here:

is the divided powers functor Ab --> Ab a Schur functor? The preprint arXiv:0910.2817, section 2.1 has details.
How about the Lie functor Ab --> Ab, which is just the tensor algebra with the obvious Z-Lie structure? Same paper for details.

David Roberts
• CommentRowNumber7.
• CommentAuthorTodd_Trimble
• CommentTimeOct 26th 2009

Thanks, David. For the time being I'm restricting to categories enriched in rational vector spaces, so for the time being let me apply the query to $Vect_{fd}$ (finite-dimensional spaces) instead of $Ab$. Then yes, it looks like their paper gives formulas for the homogeneous components of these constructions as direct sums of certain classical $S_\lambda$'s.

• CommentRowNumber8.
• CommentAuthorbwebster
• CommentTimeOct 27th 2009
• CommentRowNumber9.
• CommentAuthorTodd_Trimble
• CommentTimeOct 27th 2009

Thanks, Ben. I added a small and maybe slightly cryptic comment, to be followed up on later.

• CommentRowNumber10.
• CommentAuthorbwebster
• CommentTimeOct 28th 2009

I also created a stub on Specht modules, which should be key for defining analogues of Schur functors for all abelian monoidal categories.