Are Dwarf Galaxies a Subset of Galaxies?
The IAU has not defined &quot;galaxy&quot;, therefore you should not use the word  (Joke)
In all seriousness, language is a tool.  You are trying to dance around definitions.  There are many types of galaxies: spiral and elliptical, barred and unbarred, flocculent and unflocculent, small, medium and large.  They are all galaxies, of one kind or another.  The IAU has chosen to define &quot;Planet&quot; and &quot;Dwarf planet&quot; in a particular way, so that children don't have to learn the names of 46 solars system bodies.  They haven't chosen to give a definition of &quot;galaxy&quot;, nor &quot;cluster&quot; nor &quot;nebula&quot;.  But it doesn't matter.  You use language to communicate. You are not in thrall to the IAU. So you can use the word &quot;galaxy&quot; as they do to mean &quot;galaxy&quot;.
Yes: dwarf galaxies are galaxies.