on page $38$ of the book "Ring theory" by Louis Rowen it is shown that $R-\mathbf{Mod}$ and $M_{n}(R)-\mathbf{Mod}$ are equivalent categories ($R$ a ring). Some lines below the author states that these categories are not isomorphic, but why is this?
Equivalent categories yet not isomorphic
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0@magma: It is most likely the category of left modules over the ring of $n\times n$ matrices with entries in $R$. – 2012-10-19
1 Answers
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I guess the author might have wanted to write 'these rings are not isomorphic' instead of 'these categories are not isomorphic', and then to introduce Morita equivalence...