Prove or disprove:
If $M, N$ are Rmodule and for all $P$ Rmodule $Hom(M,P) \simeq Hom(N,P)$ then $M\simeq N$
Prove or disprove: If $M, N$ are Rmodule and for all $P$ Rmodule $Hom(M,P) \simeq Hom(N,P)$ then $M\simeq N$ 

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K. Bongartz, "A generalization of a theorem of Auslander":


