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created a stub for John Francis’ notion of factorization homology.
Was the reason you wrote
In fact the definition of factorization homotopy
that you think homology a poor relation of the real concept homotopy?
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.
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.
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…
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.
added the arXiv-reference available now
Urs, I really already knew #6, but you made it very clear, thank you.
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.
No doubt Factorization homology of stratified spaces is important, so added it to references.
Thanks for the pointer.
I added a few references to factorization homology.
added pointer to:
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