# Talk:Free object

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Mathematics rating:
 Start Class
 Mid Importance
Field:  Algebra

## 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 ${\displaystyle X}$ be an arbitrary set and consider the vector spaces over the field ${\displaystyle K}$. ${\displaystyle (F(X),h)}$ is the freely generated algebra where

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

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

## "Free universal algebras" section

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

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)