  Let $C$ be an additive category with cokernels and let Mod($C$) be the
category of additive functors from $C^{op}$ to the category Ab of abelian
groups. Let mod($C$) be the full subcategory of Mod($C$) consisting of coherent
functors. In this paper, we first study some basic properties of pseudo-kernel
of morphisms in $C$. When $C$ has pseudo-kernels, mod($C$) is abelian and then,
in this case, we study radical functors, half exact functors, left exact
functors and injective objects in mod($C$). At last, we extend the results for
Mod($C$).
