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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 $Maps(-,A)$, is naturally “dual” to homotopy in the sense that the latter is $Maps(S^n,-)$. But in the presence of closed monoidal structure, the internal hom $[-,A]$ is also naturally “dual” in another sense to the tensor $-\otimes A$, 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)

• 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 $n$Lab, 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.
• CommentTimeApr 15th 2015

I added a few references to factorization homology.

• CommentRowNumber14.
• CommentAuthorTim_Porter
• CommentTimeMar 22nd 2019

updated the last link in the page

• CommentRowNumber15.
• CommentAuthorTim_Porter
• CommentTimeJul 24th 2019

Added a link to what seem to be a useful set of videos from the workshop: Factorizable Structures in Topology and Algebraic Geometry.