Talk:Free object

Master

"It is probably better to master some special case such as free groups first."

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Correction

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

An example of a free algebra. Let $X$ be an arbitrary set and consider the vector spaces over the field $K$. $(F(X),h)$ is the freely generated algebra where

$h(x):X\longrightarrow K$. $h(x)(y)=1$ if $x=y$, $0$ otherwise.

$F(X)=\{\sigma :X\longrightarrow K|\{x\in X|\sigma (x)\neq 0\}{\mbox{ finite }}\}$

"Free universal algebras" section

Should the last part be "there exists a unique homomorphism $\sigma :\mathbf {A} \longrightarrow \mathbf {B}$ such that $\sigma \psi =\tau$."?

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)