Talk:F-algebra

1 + X

What does "1 + X" in the example mean? I (not a category theorist) assume it's the set of numbers y such that y = 1 + x for some x in X. But that only makes sense if X is a set of numbers (or I guess any ring with 1). That doesn't seem to extend very well to the entire category of sets. Staecker 02:11, 25 July 2006 (UTC)

I'm not a category theorist either, but I'm guessing it refers to the disjoint union. That is, X + Y is the union of the sets X and Y, but with the elements "relabelled" to make sure the sets don't overlap. See category of sets and coproduct to see how this idea fits into category theory.

I believe the article is wrong when it says "where 1 is some singleton subset of X". If we are indeed talking about the disjoint union then 1 can refer to any singleton set. GilesEdkins 00:22, 21 January 2007 (UTC)

I've clarified the notations of the example. I hope that they are clear now. Samuel Mimram 17:56, 22 January 2007 (UTC)

Thanks- should've known it was a coproduct. Staecker 19:32, 22 January 2007 (UTC)

Natural numbers are initial algebra?

The page claims that the natural numbers (together with [zero,succ]) are an initial algebra for Set and the functor FX = 1 + X. Is this really true? Surely there is an alegbra on an uncountably-infinite object... —Preceding unsigned comment added by 158.130.51.58 (talk) 20:36, 31 May 2010 (UTC)

Never mind, this is well explained on the (separate) page for initial algebras. —Preceding unsigned comment added by 158.130.51.58 (talk) 20:53, 31 May 2010 (UTC)

Technical?

Diego Moya has done some nice cleaning up of this article. But he added the tag Template:Technical. I think this is inherently a technical topic; I don't think someone should really hope to understand much if they don't know what a category is. Could you make some suggestions about what you think is TOO technical, where it doesn't need to be? Similarly on F-coalgebra. Thanks, ComputScientist (talk) 19:35, 21 January 2011 (UTC)

When an article is technical in nature, it still can be made accessible to a general public by placing it in context. Create an applications section like that in F-coalgebra#Applications showing examples applied to programming, explain who use this technique and what for, tell something about its history (who invented it, for what reasons)...

I don't buy the typical argument often found at mathematics talk pages that "this article surely would be useless to someone who doesn't know X". Every article has a human side even if the topic is extremely technical or abstract. An encyclopedia should aim to cover that side; to learn only about the technical details you'd use a textbook instead. The point is not that someone would understand 'much'; is that the reader could at least understand something. If someone (as myself) who doesn't know cathegory theory found this article, she must have some good reason to want to learn about it. An article written by and for mathematicians experts in the topic is useless for that reader.

(Also the technical tag was added when the lead section was a mathematical definition, something absolutely contrary to wp:lead. The changes I propose are to continue further in the direction I began at the introduction). Diego Moya (talk) 12:37, 22 January 2011 (UTC)