Rack cohomology as derived functor cohomology

Let $$X$$ be a rack and $$A$$ be an $$X$$-module. By this paper, p. 33, we can associate a cochain complex $$C^\bullet(X,A)$$ to the pair $$(X,A)$$. This complex is explicitly defined by a differential $$d$$. I wonder if the cohomology $$H^\bullet(X,A)$$ of the complex has an interpretation as derived functor cohomology. What functor from $$X$$-modules to $$X$$-modules do we have to derive? And how to show then the equivalence of the two definitions? I think the analogy to group cohomology is not very helpful, or can we somehow define the invariants of an $$X$$-module and make it fit?

• If it is a derived functor, it's the derived functor of H^0. I'm not sure if this helps though :) Apr 18 at 10:46
• You are right, thank you. Apr 18 at 11:02