Abstract:
We describe an exact embedding of a preabelian category with a fixed proper class of cokernels into an abelian category. This abelian category is constructed similar to the category used by Freyd in the embedding of an exact category (in the sense of Qullen) into the mentioned abelian category. The embedding functor constructed in the paper reflects short exact sequences. Moreover, the image of this functor is closed with respect to extensions if and only if cokernels from the given proper class are stable.
Key words and phrases:preabelian category, proper class of cokernel, Gabriel's localization theory, category of left exact functors.
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