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• CommentRowNumber1.
• CommentAuthorbwebster
• CommentTimeNov 5th 2009
• (edited Nov 5th 2009)

I thought it might be good if somebody explained the relationship between decategorification and extended TQFT. My understanding from talking to physicists is that you should multiply your space by $S^1$; is this right in a mathematical sense? I've added a query box asking roughly the same thing.

Also, I attempted to add a sidebar, mostly just to try it out, and somehow it's not rendering right. Anyone want to explain what I did wrong?

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 5th 2009
• (edited Nov 5th 2009)
This comment is invalid XHTML+MathML+SVG; displaying source. <div> <blockquote> Anyone want to explain what I did wrong? </blockquote> <p>I can't really explain it, all I can say is that the problem went away after I added closing sharp-signs not just before but also after the headlines. Not sure why that makes a difference here but not elsewhere. Probably the parser gets mixed up somhow by the inclusion process.</p> <p>Then I slightly expanded and slightly restructures the toc. Just a suggestion.</p> </div>
• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 5th 2009

I replied at decategorification. But probably one can say something better. As I said, I should really go to bed now :-)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeNov 5th 2009

replied to David Roberts at horizontal categorification

• CommentRowNumber5.
• CommentAuthorEric
• CommentTimeNov 5th 2009

I knew you couldn't resist! Get some sleep :)

• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeMay 23rd 2017

I’m removing this query:

+–{: .query} Ben Webster: Perhaps something could be said about an extended TQFT $F$? My understanding was that the decategorification of $F(X)$ was given by $F(X\times S^1)$; is this right?

Urs Schreiber: that process certainly makes an $n$-dimensional QFT becomes an $(n-1)$-dimensional one. It is pretty much exactly the mechanism of fiber integration.

So this certainly does have a flavor of decategorification. But the latter also has a precise sense in terms of taking equivalence classes in a category. So at face value fiber integration is something different. But perhaps there is some change of perspective that allows to regard it as decategorification in the systematic sense.

=–