Timeline for Is monomorphism going in both directions sufficient for isomorphism?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Sep 27, 2010 at 2:12 | comment | added | David Roberts♦ | In category theory one has to get away from thinking of objects in the way that sets are defined in ZFC. All you know about are arrows, not about how objects are 'contained in' other objects in some global sense. But once a given object is fixed, then considering subobjects of that one object is much easier and nicer. The full subcategory of C/X consisting of the monos is a poset, which means that monos representing the same subobject are canonically isomorphic in this slice category, but not in C. | |
| Jul 21, 2010 at 23:07 | comment | added | Martin Brandenburg | No, Schröder-Bernstein does NOT hold in most cases. | |
| Jul 21, 2010 at 12:18 | comment | added | Seamus | OK. But in general it is not true that subobjecthood determines and antisymmetric relation? But in most cases of interest, it will... | |
| Jul 19, 2010 at 7:32 | comment | added | Martin Brandenburg | you're right, but this is not really a misbehavior of subobjects. since when you fix some object $X$, then the subobjects of $X$ behave well (see my answer). | |
| Jul 18, 2010 at 21:35 | comment | added | Seamus | Here's the worry: in the two object category I defined above, each of A and B is a subobject of the other, but they are not isomorphic. Is this just a case where the categorical notion of "subobject" doesn't make sense, or have I misunderstood? | |
| Jul 18, 2010 at 20:15 | comment | added | Seamus | I don't know what you mean by "the morphisms ... over X are uniquely determined" | |
| Jul 18, 2010 at 17:53 | comment | added | Martin Brandenburg | I don't know which mono you mean, but nowhere uniqueness of something is required. | |
| Jul 18, 2010 at 17:43 | comment | added | Seamus | So to get this straight: the definition of subobject requires that the monomorphism be unique? | |
| Jul 18, 2010 at 17:30 | history | answered | Martin Brandenburg | CC BY-SA 2.5 |