Frey's theorem states that every Abelian category is a subcategory of some category of modules over a ring. Mitchell (1964) has strengthened this, saying every Abelian category is a full subcategory of a category of modules over a ring.

# Freyd's Theorem

## See also

Abelian Category
*This entry contributed by John Renze*

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## References

Freyd, P.*Abelian Categories: An Introduction to the Theory of Functors.*New York: Harper & Row, 1964.Mitchell, B. "The Full Imbedding Theorem."

*Amer. J. Math.*

**86**, 619-637, 1964.

## Referenced on Wolfram|Alpha

Freyd's Theorem## Cite this as:

Renze, John. "Freyd's Theorem." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/FreydsTheorem.html