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Tim Campion (Nov 05 2023 at 00:13):I'm looking for a copy of
Renato Betti and Massimo Galuzzi. Categorie normate. Boll. Un. Mat. Ital. (4), 11(1):66–75, 1975.
I believe the journal abbreviation is for Bollettino dell'Unione Matematica Italiana. My library claims to have a physical copy, but they need to fetch it from off-campus and I am impatient :) Many back-copies are available from the union itself here, but unfortunately there's a gap between 1968-1997. It appears to be the same set of issues available on EuDML. The Springer website only has issues since 2014. My other favorite sources are failing me too.
The paper was cited by Neeman and purportedly contains a fuller discussion of "normed categories", which were alluded to by Lawvere but are less well-known than the Lawvere metric spaces which Lawvere discussed more fully (and famously) in the same paper. A normed category has a set of morphisms for each pair of objects and additionally each morphism is assigned a length (a real number) subject to some axioms. I'm interested in seeing these ideas fleshed out, hopefully in a way complementary to Kubis.
David Michael Roberts (Nov 05 2023 at 08:31):Have you asked Neeman? He's very approachable.
Nathanael Arkor (Nov 05 2023 at 10:53):The union itself might be willing to scan a copy too.
Nathanael Arkor (Nov 05 2023 at 10:54):I had also wanted to take a look at this paper; if you do get a copy, might you be able to upload it to the nLab or somewhere like that?
Bryce Clarke (Nov 05 2023 at 22:02):I recall @Paolo Perrone citing this paper in one of his preprints; maybe he has a copy on hand?
Tim Campion (Nov 06 2023 at 20:40):Thanks all! I have a physical copy now, but the binding is such that I can't make a legible scan to upload. I will probably bring it back to the library and ask them to scan it for me. It is indeed in Italian.
Paolo Perrone (Nov 07 2023 at 09:30):Bryce Clarke said:
I recall Paolo Perrone citing this paper in one of his preprints; maybe he has a copy on hand?
I do have a a copy, does anyone want it?
Also, if you need a translation of some parts, I can help.
Tim Campion (Nov 08 2023 at 15:31):Betti-Galuzzi-1975-Categorie-normate.pdf
Here's a copy from Richard Garner. As far as I can tell, it's nothing earth-shattering -- they confirm my hunch that the category to enrich in is , and observe that you can enrich in for any .