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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

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Does base extension reflect the property of being isomorphic?

I hope I'm not misunderstanding the question. Here goes: We'll show that if $M,N$ are finite-dimensional over $K$, then they are isomorphic over $K$. Think of the linear space $X=\mathrm{Hom}_{A}( …
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