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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 30th 2012

    created a stub for John Francis’ notion of factorization homology.

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 30th 2012

    Was the reason you wrote

    In fact the definition of factorization homotopy

    that you think homology a poor relation of the real concept homotopy?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 30th 2012

    Woops. My fingers once again. They begin to lead a life of their own. ;-)

    Concerning your question: I see what you mean, but I am not quite sure. I need to learn/think about this a bit more.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 31st 2012

    My question derived from judgements such as here:

    homology in turn seems to be a rather contrived, rather derived concept… it appears as a comparatively ad hoc, comparatively unnatural thing to consider.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 31st 2012

    Just sat in the second talk by John Francis, used the occasion to fill some of my notes into the entry factorization homology.

    David, yes, I know what you mean. I’ll reply in more detail a little later, don’t have the time right now…

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 31st 2012
    • (edited Jun 28th 2012)

    David, very briefly, in a stolen second:

    Cohomology, being Maps(,A)Maps(-,A), is naturally “dual” to homotopy in the sense that the latter is Maps(S n,)Maps(S^n,-). But in the presence of closed monoidal structure, the internal hom [,A][-,A] is also naturally “dual” in another sense to the tensor A-\otimes A, hence to homology. So homology is quite naturally dual to cohomology for given chosen monoidal structure. That’s how it works.

    • CommentRowNumber7.
    • CommentAuthorjim_stasheff
    • CommentTimeMay 31st 2012
    So one is no more unnatural than the other?
    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 27th 2012
    • (edited Jun 27th 2012)

    added the arXiv-reference available now

    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeJun 28th 2012

    Urs, I really already knew #6, but you made it very clear, thank you.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 29th 2012

    Okay, if this is missing on the nnLab, it needs to be added. I started making an attempt, but let’s discuss this in its own thread, here.

    • CommentRowNumber11.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 8th 2014

    No doubt Factorization homology of stratified spaces is important, so added it to references.

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeSep 9th 2014

    Thanks for the pointer.

    • CommentRowNumber13.
    • CommentAuthoradeelkh
    • CommentTimeApr 15th 2015

    I added a few references to factorization homology.

    • CommentRowNumber14.
    • CommentAuthorTim_Porter
    • CommentTimeMar 22nd 2019

    updated the last link in the page

    diff, v15, current

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