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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

    Iā€™m removing this query:

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

    Urs Schreiber: that process certainly makes an nn-dimensional QFT becomes an (n1)(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.


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