A topological leftmodule $_CX$ is a topological functor $C \to Top$ for a Category $C$. A morphism $_CX \to _CY$ of leftmodules is a natural transformation of functors.
Now such a morphism is called an equivalence if it is a strong homotopy equivalence in the category of $C$-Modules.
But how is a strong homotopy equivalence in the category of C-Modules defined?