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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 10th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have split off an entry [[epi/mono factorization system]] in order to better be able to amplify the higher pattern that this sits in

   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

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeOct 10th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexIt 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 ?

   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 ?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeOct 10th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe slash seems more suggestive notation to me. But I don't mind if you change it.

   The slash seems more suggestive notation to me. But I don’t mind if you change it.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeOct 10th 2011
   • (edited Oct 10th 2011)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI 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 $(L,R)$ 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 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 $(L,R)$ 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.

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeOct 11th 2011
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI 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]].

   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.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeOct 11th 2011
   • (edited Oct 11th 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexAs 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.

   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.

7. • CommentRowNumber7.
   • CommentAuthorTobyBartels
   • CommentTimeOct 11th 2011
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexFor 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.

   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.

8. • CommentRowNumber8.
   • CommentAuthorTodd_Trimble
   • CommentTimeOct 11th 2011
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexHyphens would definitely be worth it.

   Hyphens would definitely be worth it.

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeOct 11th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexOh, I see! :-)

   Oh, I see! :-)

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeOct 11th 2011
    • PermaLink
    Author: Urs
    Format: MarkdownItexI have renamed it to [[(eso+full, faithful) factorization system]]

    I have renamed it to (eso+full, faithful) factorization system

11. • CommentRowNumber11.
    • CommentAuthorzskoda
    • CommentTimeOct 11th 2011
    • PermaLink
    Author: zskoda
    Format: MarkdownItexgreat

    great

12. • CommentRowNumber12.
    • CommentAuthorMike Shulman
    • CommentTimeOct 11th 2011
    • PermaLink
    Author: Mike Shulman
    Format: MarkdownItexShould 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?

    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?

13. • CommentRowNumber13.
    • CommentAuthorzskoda
    • CommentTimeOct 11th 2011
    • PermaLink
    Author: zskoda
    Format: MarkdownItexI think this is the most clear option as the default. We still need some other redirects.

    I think this is the most clear option as the default. We still need some other redirects.

14. • CommentRowNumber14.
    • CommentAuthorMike Shulman
    • CommentTimeOct 11th 2011
    • PermaLink
    Author: Mike Shulman
    Format: MarkdownItexI renamed (epi, mono), (bo, ff), and also (geometric surjection, embedding).

    I renamed (epi, mono), (bo, ff), and also (geometric surjection, embedding).

15. • CommentRowNumber15.
    • CommentAuthorTobyBartels
    • CommentTimeOct 12th 2011
    • PermaLink
    Author: TobyBartels
    Format: MarkdownItexI like it!

    I like it!