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Is there way to see $L^1$ a functor from the category with objects as metric measure spaces $(X,d,\mu)$ and morphisms Lipschitz maps to the category of Banach spaces (or something which has a forgetful functor to the category of topological vector spaces)?

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  • $\begingroup$ You might be interested by these slides of Tom Leinster, especially the second part. This short note is more related to the first part, but might contain a few useful remarks. $\endgroup$ – Arnaud D. Apr 25 at 6:37
  • $\begingroup$ Indeed, I have come across these last evening. Do you happen to know if there is an acompanying paper? It seems that there are few citations $\endgroup$ – AIM_BLB Apr 25 at 7:49
  • $\begingroup$ I don't think there is; at least there is no paper on this subject listed on his webpage (where I found the other links). There is an nCafé post though. $\endgroup$ – Arnaud D. Apr 25 at 8:21
  • $\begingroup$ This is interesting. I'll send him a mail then I guess, thanks Arnaud :) $\endgroup$ – AIM_BLB Apr 25 at 9:48

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