# Lp space is a Hom functor

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)?

• 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. – Arnaud D. Apr 25 at 6:37
• 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 – AIM_BLB Apr 25 at 7:49
• 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. – Arnaud D. Apr 25 at 8:21
• This is interesting. I'll send him a mail then I guess, thanks Arnaud :) – AIM_BLB Apr 25 at 9:48