Irish monarchs are only those people who are principally considered monarchs of Ireland, not also those who have a claim to the Irish crown through the British crown. For instance, Victoria shouldn't be listed here, even though she was in fact Queen of Ireland. Sitric Silkbeard would be considered an Irish monarch – even though he didn't rule all of Ireland — by virtue of being King of Dublin.

This is not a political statement, but merely an organisational one. It simply prevents recursion in the category tree if we keep the constituent parts of the United Kingdom separate.

Note that this stance applies only to categories. Within the article about Victoria, for instance, one should mention that she was Queen of Ireland, because that point is made in Tooth and Claw.

Think of this category as meaning, "people who were only a King or Queen of (some part of) Ireland".