Zoran, I'm not sure I understand what general connection you have in mind. I guess I tend to think of such a connection as factoring through the realization functor from motives to Galois representations, and thus going through well-understood mathematics.

]]>As groupoidification appeared today again on the cafe, I have updated links, including the sbseminar links at Hecke algebra. I wish we had also a meaningful entry on Hall algebra but I am running out of time with so many things on the plate and other important deadlines approaching by this weekend.

We should also understand the general connection between the motivic functions and groupoidification.

]]>yeah, I decided it would probably be better to call that "multiplication by the motivic integral of $\mathbb{A}^1$."

]]>Thanks for this entry!

I edited it a bit (made the Theorem environment say "Theorem") and added some further links, for instance to motive.

One question: you write "the motive of " is pulling up through the projection and then pushing down along it again.

What is the terminology here: is this *operation* itself called a motive?

(All I know about motives comes from a very superficial encounter with Voevodsky's lecture notes.)

]]>David Roberts ]]>

David Roberts ]]>

Oh, the one part I was a bit unsure of is the question about a "groupoid of fintie sets" I meant a groupoid whose arrows and morphisms are finite, with no additional structure. Does "a groupoid of finite sets" mean something other than that?

]]>Ok, I think I've addressed your questions, so I deleted the query box. Thanks, by the way; I'm sure the notation is still ghastly, but somehow the work "nerve" had slipped from my mind, and I didn't know about \rightrightarrows.

]]>David Roberts ]]>

Taking the advice that if I write something on the internet, it should be stuck on the n-Lab, I've converted my recent comments in the n-category cafe and some old blog posts into a new page on the relationship between categorification and groupoidification: categorification via groupoid schemes

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