Imbedding of Abelian Categories Author(s): Saul Lubkin Reviewed work(s): Source: Transactions of the American Mathematical Society, Vol. 97, No. 3 (Dec., 1960), pp. 410-417 Published by: American Mathematical Society Stable URL: http://www.jstor.org/stable/1993379 . Accessed: 15/01/2013 15:24 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact
[email protected]. American Mathematical Society is collaborating with JSTOR to digitize, preserve and extend access to Transactions of the American Mathematical Society. http://www.jstor.org This content downloaded on Tue, 15 Jan 2013 15:24:14 PM All use subject to JSTOR Terms and Conditions IMBEDDING OF ABELIAN CATEGORIES BY SAUL LUBKIN 1. Introduction. In this paper, we prove the following EXACT IMBEDDING THEOREM. Every abelian category (whose objects form a set) admits an additive imbedding into the category of abelian groups which carries exact sequences into exact sequences. As a consequence of this theorem, every object A of (i has "elements"- namely, the elements of the image A' of A under the imbedding-and all the usual propositions and constructions performed by means of "diagram chas- ing" may be carried out in an arbitrary abelian category precisely as in the category of abelian groups.