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Kevin Carlson (Dec 03 2025 at 17:47):In his paper on composing modules between lax functors, Paré introduces a factorization property for a double category he calls "AFP." The capitalization makes this look like an initialism, but I'm a bit nonplussed to see that Paré doesn't give any obvious hints as to the origin of this rather opaque naming in the paper. The only other literature I'm aware of in which the condition is mentioned is Nathanael's recent work on exponentiable VDC's, so this may be a @Nathanael Arkor question. Does anybody have any insight on this naming, or shall I try to ask Paré directly?
Nathanael Arkor (Dec 03 2025 at 18:05):"AFP" stands for "A Factorization Property", which is the title of the section in which the condition is introduced.
Nathanael Arkor (Dec 03 2025 at 18:07):It goes without saying that this is not a good name. Something like "unary–globular decomposition property" would be more descriptive (albeit more of a mouthful).
Nathanael Arkor (Dec 03 2025 at 18:08):(It would be nice if there was a sense in which the AFP condition was canonical, which could suggest appropriate terminology.)
fosco (Dec 03 2025 at 21:15):Nathanael Arkor said:
It goes without saying that this is not a good name. Something like "unary–globular decomposition property" would be more descriptive (albeit more of a mouthful).
u.glo.de.p