Equivalent categories yet not isomorphic
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?
Solution 1:
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...