# Freyd-Mitchell Embedding Theorem

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## Theorem

Let $\AA$ be a small abelian category.

Then there exists a ring with unity $R$ and a fully faithful and exact functor $F : \AA \to R \text{-} \mathbf{Mod}$ to the category of left $R$-modules.

## Source of Name

This entry was named for Peter John Freyd and Barry M. Mitchell.