Talk:Subobject

Category of commutative rings

In the category of commutative rings, quotient objects are not right. For example, the inclusion $\mathbb {Z} \hookrightarrow \mathbb {Q}$ is a non-surjective epimorphism. GeoffreyT2000 (talk) 17:55, 9 February 2015 (UTC)[reply]

Renaming of article

I propose that the name of this article be changed to "Subobjects and Quotient Objects" since there is no article for quotient objects (and indeed there is no need for one). I don't know how to change the name of an article myself however, or if I even have the privileges to do so. Joel Brennan (talk) 12:35, 2 April 2020 (UTC)[reply]

@Joel Brennan: When an article is about a category theory topic and its dual equally, this would be a reasonable move to make. However, the resulting title should be "Subobject and quotient object" (singular and sentence case, see WP:TITLEFORMAT). As far as how to do it, see H:MOVE. Since your account is autoconfirmed, you can move pages. Since there's nothing in the way of the new title, there, there's no technical reason why you won't be able to. If there were, you could list it at WP:RM/TR (if non-controversial, like this one probably), or at WP:RM to start a discussion. Twinkle makes it making move requests even easier (although it's hidden under XfD for some reason). –Deacon Vorbis (carbon • videos) 13:17, 2 April 2020 (UTC)[reply]

Clarity could be improved

I'm making this note here in case someone would like to improve the clarity of this page. Currently, it starts by saying "a subobject is, roughly speaking, an object that sits inside another object in the same category", but this rough characterisation is never really cashed out. The definitions section starts by talking about monomorphisms and their isomorphism classes, but never quite explains why those should be thought of as "an object sitting inside another object".

Consequently, I think it would be helpful to have some motivation in between the current lede and the current definitions section, explaining that monomorphisms can be thought of as a way of embedding one object inside another (perhaps using sets as an example) and explaining why you really identify isomorphic subobjects instead of keeping them separate. I might do it myself if I have time but thought this note might be helpful in case anyone else wants to do it.

Nathaniel Virgo (talk) 03:56, 15 November 2021 (UTC)[reply]

@Nathanielvirgo: Your point is well taken. My impression is that the unclearity actually goes back to the (one and only) source for this article, namely, Saunders Mac Lane's "Categories for the working mathematician". I just checked the presentation here with the source (although with the first rather than the second edition of Mac Lane's fundamental work); and Mac Lane does essentially the same thing as this article does. He starts by referring to some well-known subobjects in some concrete categories, as subsets with structures inherited from the larger object; and then continues with a definition which explicitly does not give objects in the original category, but rather in a kind of comma category. There should be a functor involved, with the original category as codomain; but Mac Lane does not give this, at least not in a direct connection with his introduction of the concept.

Actually, I think that it would be better first to give some concrete algebraic example, then continue with the present presentation (following Mac Lane), and finally briefly connect the two approaches. JoergenB (talk) 21:59, 12 July 2024 (UTC)[reply]