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I have split off an entry epi/mono factorization system in order to better be able to amplify the higher pattern that this sits in
It is usually spelled as “epi-mono factorization system” in the category theory literature, rather than epi/mono. I would interpret slash in general as “or” (for choosing options, like “bring your husband/wife along”). Not very important, but is this change of writing intentional ?
The slash seems more suggestive notation to me. But I don’t mind if you change it.
I just think we should follow the traditional literature (we still have too little support from category theorists mainstream), at least not to confuse students (unless we can replace all the traditional literature, what we can not). A priori it would be maybe equally good for an informal seminar. Formally of course one has notation (In parallel discussion phrase essentially surjective and full/faithful factorization system is a bit confusing as it looks at first like full is contrasted to faithful. Pair notation is more precise: (essentially surjective on objects and full, faithful). I would say descriptively essentially surjective on object and full functor followed by faithful functor. Somehow it would be nice to have it more smooth and simultaneously not to hurt the traditional conventions.
I agree with Zoran. We already have bo-ff factorization system, although apparently that hadn’t made it into the examples list at orthogonal factorization system. Also, I’m sort of against using slashes in page names at all, because it makes for confusing URLs.
I added some more general comments to epi/mono factorization system.
As I said, I have no objections to changing it.
I have changed some occurences now. But since you have stronger opinions on this than I do, I would like to ask you (two) to deal with the term for the eso+full/faithful system. The choice “eso+full-faithful” that would follow from the convention that you prefer seems to forbid itself.
But I really don’t mind either way.
For what it’s worth, I keep reading “essentially surjective and full/faithful” as eso-ff, which apparently is not what you mean. Spaces around the slash may help. Also, hyphens between many-word phrases can be turned into en dashes, which can make them easier to read.
Hyphens would definitely be worth it.
Oh, I see! :-)
I have renamed it to (eso+full, faithful) factorization system
great
Should we make that the standard naming convention for factorization systems? So epi-mono factorization system should be (epi, mono) factorization system and likewise for bo-ff?
I think this is the most clear option as the default. We still need some other redirects.
I renamed (epi, mono), (bo, ff), and also (geometric surjection, embedding).
I like it!
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