Talk:Free object

Master

"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

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)