K-theory for triangulated categories 3 1/2 (A): 
A detailed proof of the theorem of homological
functors

Amnon Neeman

Abstract. 
Let $\mathcal A$ and $\mathcal B$ be abelian categories.
Let $H:\mathcal A\rightarrow\mathcal B$ be a bounded
$\delta$-functor. We prove that $H$ induces a natural
map in higher K-theory. From a more precise analysis of
the proof, we deduce that it is possible to define a
K-theory of the bounded derived category of $\mathcal A$,
which contains Quillen's K-theory of $\mathcal A$ as a
retract.