Talk:Free object
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Master
[edit]"It is probably better to master some special case such as free groups first."
This suggestion does not have any content bearing on the topic.
I agree. I'll cut that.--345Kai (talk) 22:59, 8 May 2009 (UTC)
Correction
[edit]The first section, the introduction, glosses a point: the set of words is the appropriate starting point only for associative algebras, otherwise, it needs to be the magma of binary trees. I will clarify/fix this later; I am going to an Easter party now. linas 18:03, 8 April 2007 (UTC)
- Have a good time. I've added a note covering this issue. Charles Matthews 18:29, 8 April 2007 (UTC)
Free universal algebras
[edit]An example of a free algebra. Let be an arbitrary set and consider the vector spaces over the field . is the freely generated algebra where
. if , otherwise.
"Free universal algebras" section
[edit]Should the last part be "there exists a unique homomorphism such that ."?
Otherwise, I don't know where the sigma came from or what it's supposed to mean.--kundor (talk) 14:18, 8 July 2008 (UTC)
Examples
[edit]The main example of a free group is very confusing with respect to the formal definition. What corresponds to , , and in the example? Why does have a subscript 2? — Preceding unsigned comment added by Eposse (talk • contribs) 16:26, 31 May 2020 (UTC)
- The notation refers to the Free group with 2 generators a and b. The set X is the set of generators, here {a, b}. In section "Definition", A denotes the free object, here anf i is the injection of X in A, which, here, maps a and b viewed as elements of the set X to themselve viewed as elements of the free group.
- I agree that the article is badly written, in a pedantic style (systematic use of technical terms that are not mastered by most readers, the same thing can be comprehensibly said with few more words). D.Lazard (talk) 17:38, 31 May 2020 (UTC)
Bug in the Definition?
[edit]What is the parameter $A$ in the term $F(A)$ in the definition? I guess it should be rather $F(X)$... So all $X$ or all $A$ 2A01:598:D007:4610:74C9:8F80:2E52:CA5F (talk) 15:04, 1 July 2022 (UTC)
- A is the free object to be defined. However, I'll clarify that X is a set and A is an object of C. D.Lazard (talk) 16:11, 1 July 2022 (UTC)
Upgrading to tikz diagram
[edit]@D.Lazard I noticed that you reverted a few changes. Could you explain a bit? For example, I thought it made sense to upgrade the commutative diagram to tikz for consistency with universal property. Davidvandebunte (talk) 17:37, 1 April 2023 (UTC)
- Sorry, I did not see that you did edit yestersay. I intended to revert the edits of today, concerning nlab references. I have restored your edits that are not for linking nlab. The removal of these links is explained in WP:USERGENERATED. D.Lazard (talk) 17:57, 1 April 2023 (UTC)
- OK thanks, that makes sense. I've generally made exception for nlab because it is usually edited by authoritative authors in category theory like John Baez, and I'd seen it used as a reference in other articles (see Adjoint functors). But, I can see your point. Perhaps this could go under an "External links" section as in Category theory? Davidvandebunte (talk) 18:19, 1 April 2023 (UTC)