Some fundamental results on K0 of exact and Abelian cate- gories – with applications to orders and grouprings

In the following section we discuss some of the results whose higherdimensional analogues will be given when higher K-groups are treated in chapter 6.

Definition 2.1.1 Let C0 ⊂ C be exact categories. The inclusion functor C0 → C is exact and hence induces a homomorphism K0(C0) → K0(C). A C0filtration of an object A in C is a finite sequence of the form: 0 = A0 ⊂ A1 ⊂ · · · ⊂ An = A where each Ai/Ai−1 ∈ C0.