Abstract
In this paper, we obtain a non-abelian analogue of Lubkin's embedding theorem for abelian categories . Our theorem faithfully embeds any small regular Mal'tsev category C in an n -th power of a particular locally finitely presentable regular Mal'tsev category. The embedding preserves and reflects finite limits, isomorphisms and regular epimorphisms , as in the case of Barr's embedding theorem for regular categories. Furthermore, we show that we can take n to be the (cardinal) number of subobjects of the terminal object in C .
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