How do we define the tensor functor

Question

In my course, the teacher defines the tensor functor $$-\otimes-:\text{Mod}_K\times \text{Mod}_K\rightarrow \text{Mod}_K : (M,N)\mapsto M\otimes N$$ but he does not define how the functor acts on functions $f:(M,N)\rightarrow (M',N')$

How could one define this?

Answer 1

By $$(f\otimes g)(x\otimes y) = f(x)\otimes g(y)\ .$$