Talk:Group object
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Are linearly ordered groups an example of the sort of thing this is about? Michael Hardy 01:04, 1 Dec 2003 (UTC)
- Those would have to be group objects in the category of partially ordered sets with order-preserving functions as morphisms. Note that the category is that of partially ordered sets because the product of two linearly ordered sets is naturally partially ordered, but not linearly ordered. There is another glitch, though, as the inverse operation reverses the order, so we need to add the order-reversing morphisms to the category. It seems to be easier to just talk about ordered monoids. -- Miguel
[edit] Subgroup objects
Near the bottom of the article it talks about how most of group theory can be transfered over to group object theory. It uses subgroups and normal subgroups as examples. I do not understand how subgroups could be transfered over. The only way I could think of is to say a subgroup object is a subobject of a group object that follows the group object identities in the article but that won't work because a subobject isn't a object in its own right. It's a equivilence class of monomorphisms with codomain G! It just doesn't make sense. Possibly, someone out there can clarify this and put it in the article.--SurrealWarrior 22:56, 14 December 2006 (UTC)
