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