Let $L/K$ be a Galois extension over the field $K$. Is it true that $$\text{Hom}_K(L,\text{Hom}_L(L,L)) \cong \text{Hom}_K(L,L)?$$
Any ideas to start me off would be great. Would it come down to showing that $L \cong \text{Hom}_L(L,L)$?
Let $L/K$ be a Galois extension over the field $K$. Is it true that $$\text{Hom}_K(L,\text{Hom}_L(L,L)) \cong \text{Hom}_K(L,L)?$$
Any ideas to start me off would be great. Would it come down to showing that $L \cong \text{Hom}_L(L,L)$?
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