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Reference.org
Mitchell's embedding theorem
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<p>Mitchell's embedding theorem, also known as the Freyd–Mitchell theorem or the full embedding theorem, is a result about <a href="/facts/Abelian_category/4WN473Yc">abelian categories</a>; it essentially states that these categories, while rather abstractly defined, are in fact <a href="/facts/Concrete_category/4vYnbnjq">concrete categories</a> of <a href="/facts/Module_(mathematics)/jP0LIhFL">modules</a>. This allows one to use element-wise <a href="/facts/Diagram_chasing/bdG8xuer">diagram chasing</a> proofs in these categories. The theorem is named after Barry Mitchell and <a href="/facts/Peter_Freyd/jbQAncXD">Peter Freyd</a>. </p>