Talk:Subobject

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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]