How can this be a complex if each term isn't an abelian group?

Question

I'm reading self learning Algebraic Topology from Rotman's Introduction to Algebraic Topology and I've come across this:

In the book previously a complex is defined as a sequence of abelian groups, but here each $E$ functor is defined as a map to $\text{Comp}$.

How can the $EC$ complex be a complex since each $E_kC$ is an element of Comp and not an abelian group?