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Drew Armstrong
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Can one characterize the category of finite-dimensional vector spaces?

Let $K$ be a field. Does the category of finitely generated $K$-modules have a nice characterization, for example as the unique abelian category satisfying a certain simple condition? For example, we know that:

  1. Every short exact sequence is split.
  2. The Euler characteristic of every bounded exact sequence is zero.

Are either of those enough to characterize the category?

Drew Armstrong
  • 3.8k
  • 19
  • 41