Timeline for The cofibration/fibration $\leftrightarrow$ epi/mono confusion
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2017 at 10:43 | vote | accept | მამუკა ჯიბლაძე | ||
| Nov 30, 2017 at 21:46 | answer | added | Yonatan Harpaz | timeline score: 9 | |
| Nov 30, 2017 at 14:44 | answer | added | Simon Henry | timeline score: 10 | |
| Nov 30, 2017 at 14:39 | comment | added | მამუკა ჯიბლაძე | @ChrisSchommer-Pries It would be great if you could elaborate in an answer. Are there such (mono,epi) examples with some amount of uniqueness? I mean, in model categories the two classes do in a sense (although not without involvement of weak equivalences) determine each other, and moreover there is even some amount of uniqueness of liftings involved (again up to weak equivalences), just as in the orthogonal case. Is something similar observed in the (mono,epi) context? | |
| Nov 30, 2017 at 14:36 | comment | added | Chris Schommer-Pries | I would say that there is an "obvious resemblance" between model categories and weak factorization systems, while what you describe, the (epi,mono) system, is an orthogonal factorization system. Orthogonal factorization systems are very special. For weak factorization systems (mono, epi) on set is a perfectly good example with generic features. See ncatlab.org/nlab/show/weak+factorization+system | |
| Nov 30, 2017 at 14:27 | history | asked | მამუკა ჯიბლაძე | CC BY-SA 3.0 |