We describe a criterion for a natural Euler characteristic that takes values in a relative algebraic K 0-group to be additive in distinguished triangles. As preliminary steps we prove several results about determinant functors, in particular concerning the comparison of the determinant of a complex to the determinant of its cohomology.
"Additivity of Euler characteristics in relative algebraic $K$-groups." Homology Homotopy Appl. 7 (3) 11 - 36, 2005.