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For any set we can construct a free group on it. Also for non associative structures like Lie algebra, Lie ring we may construct free structures, but these are non associative structures and having two binary operations among which one is associative.

My question is

Can we construct a free structures on any non associative algebraic structure (where we can give a weaker condition like association).

One example of such algebraic structure is the gyrogroup (for definition see https://groupprops.subwiki.org/wiki/Gyrogroup).

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    $\begingroup$ You can search about universal algebra, an area that deals with these kinds of questions, but for all algebraic structures. In particular, we have free gyrogroups, and the construction is the same for every free algebraic structure. $\endgroup$
    – Trebor
    Commented Jun 15 at 6:12
  • $\begingroup$ Thanks for your comment. Can you give some references? $\endgroup$
    – MANI
    Commented Jun 23 at 6:42

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