Talk:Initial and terminal objects

Mathematics Stub‑class Mid‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
Stub	This article has been rated as Stub-class on Wikipedia's content assessment scale.
Mid	This article has been rated as Mid-priority on the project's priority scale.

Rename to universal object?

What do people think about renaming this page to universal object? The primary advantage is that this name treats initial and terminal objects on equal footing. After all, this article is just as much about terminal objects (and zero objects) as it is initial objects. The primary disadvantage is that the name universal object is not nearly as common as initial or terminal object. It is, however, used in this sense—see, for example, Lang's Algebra or Hungerford's Algebra. Numerous other instances can be found (excepting, notably, Mac Lane's monograph).

I would still suggest we use the terminology initial object and terminal object in the article itself. Which of these should be universal and which should be couniversal is surely going to vary from author to author. Hungerford, for example, calls initial objects universal and terminal ones couniversal, but this is at odds with the usage of limits and colimits. Lang calls initial objects universal repelling and terminal objects universally attracting which is slightly more descriptive. -- Fropuff (talk) 19:47, 15 January 2008 (UTC)[reply]

zero group

why is the empty set initial in set, but not in group?