Is this a cool-toned blue?

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Its not cobalt. It has a purply hue.

With hoc, any colour with yellow tones in It is warm, i.e. Khaki. Whereas colours with blue in them are cool, e.g. Pine green. An example of green being both warm and cool depending on the hue.
Blues like teal which have yellow in them are warm and blues which have none are cool. Pinks can be cool too as long as they're based on blue. Red lipsticks which are blue based not orange based work for hoc winters and summers as they are cool. The colour wheel
Is here

So that's the opposite of the artist's colour wheel I posted earlier. As I said, it@s all just theory. Checking, yellow makes blue cool in art theory, but according to hoc it makes it warm. Red makes it warm for an artist. It's not so much adding the colour, it's more the position on the colour wheel relative to the primary.

Thanks everyone. Sounds confusing!

For makeup, I suit blue-based pinks. I know blue works for me, but there are certain shades of blue that don't. Browns and greens, I look so bad when I wear them.