nLab noncommutative motives - table

geometric context	universal additive bivariant (preserves split exact sequences)	universal localizing bivariant (preserves all exact sequences in the middle)	universal additive invariant	universal localizing invariant
noncommutative algebraic geometry	noncommutative motives $Mot_{add}$	noncommutative motives $Mot_{loc}$	algebraic K-theory	non-connective algebraic K-theory
noncommutative topology	KK-theory	E-theory	operator K-theory	…