An embedding theorem for regular Mal'tsev categories

作者：Jacqmin Pierre Alain^*

来源：Journal of Pure and Applied Algebra, 2018, 222(5): 1049-1068.

DOI：10.1016/j.jpaa.2017.06.006

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.

• 出版日期2018-5