Is there such a thing as a free quasivariety?

Question

I have heard in universal algebra there is such a thing as a free variety, but is there such a thing as a free quasivariety? I would assume, that, for instance, in the language of a single binary operation symbol $*$, a free quasivariety is a free variety where additionally if $x*y=z*w$, then $x=z$ and $y=w$. Is this correct?

Answer 1

There are no such concepts as "free variety" or "free quasi-variety" in Universal Algebra. There are free objects in a variety (quasi-variety).