There are many references to Domain, Codomain, Morphism, Object, etc. which already have pages set up for them in the context of set theory and abstract algebra. These pages need to be linked to (partly done) and then added to (to put the category-specific information in there) and then the alternative notation expounded upon. This is work in progress but I'm probably not in a position to do it myself, all I know about category theory is one book I read and what's on Wikipedia. --prime mover 00:41, 17 February 2011 (CST)
I'll write what I can, my hesitation is that I'm used to categorical language, but until now hadn't considered how to formalise Classes. MacLane describes several different approaches quite clearly so I'll probably follow him. I'll work on the related pages once this page and Def:Class are written Linus44 05:11, 17 February 2011 (CST)
I think it is better to give a general definition of category making some emphasis that morphisms need not necessarily functions. I think that talking about small categories should not be in this page, it needs another page, with links about sets, classes and conglomerates. If the reader is not acquainted with results like the Russell paradox, what is a set, etc. this is only confusing.
This definition needs more work, I think is better to talk about the one with objects, that is more simple.
I am new in this site, it is nice to be able to write in LaTeX, but the message warning about some problem in converting to png, is some intimidating.
- If you don't want the png message, then set up a user account. Once you do that, you won't get the captcha. We like to know who we are talking to.
- I am sorry I rolled back your contribution, but the properties you added are already in the wiki under the morphism page. That's how we organise things on this site. --prime mover 16:28, 16 May 2011 (CDT)
I moved the set versus class stuff to Definition:Class (Class Theory); since there's several ways of comprehending classes. I think it's better there, since that page is more suited to a more encyclopedia-like page style. --Linus44 22:31, 15 June 2011 (CDT)
...that this definition does not really contribute a lot towards the understanding of a category in general, and sits in the place where metacategory naturally belongs. We already have Definition:Small Category to deal with foundational aspects. Otherwise, the definition currently up may simply be moved to Definition:Category/Set Theory. For comparison, one wouldn't want to be calling things a metaset all the time when in naive set theory (as opposed to sets existing only in a model of ZF). But then, maybe this fine distinciton is well worth keeping because it allows to easily show that categorial foundations for set theory would not be circular. --Lord_Farin 11:08, 9 August 2012 (UTC)
- Nah forget that. I shouldn't be placing laziness above rigour. Again, disregard the above suggestion please. --Lord_Farin 11:09, 9 August 2012 (UTC)