@Ness2000 @Tfmonkey No. The seven deadly sins do not map to the trichotomy because they aren't sins unless you accept such definitions; they are byproducts of human nature and scarcity.
You don't have to be an individualist to be afflicted by envy or by wrath, even primarily. Republicanism doesn't make sense being mapped to gluttony; gluttony shouldn't even be separated from greed because it's a specific kind of greed (though this is an criticism of the classifications themselves).