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Variations of the Shifting Lemma and Goursat categories
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Orientador(es)
Resumo(s)
We prove that Mal'tsev and Goursat categories may be characterized through variations of the Shifting Lemma, that is classically expressed in terms of three congruences R, S and T, and characterizes congruence modular varieties. We first show that a regular category C is a Mal'tsev category if and only if the Shifting Lemma holds for reflexive relations on the same object in C. Moreover, we prove that a regular category C is a Goursat category if and only if the Shifting Lemma holds for a reflexive relation S and reflexive and positive relations R and T in C. In particular this provides a new characterization of 2-permutable and 3-permutable varieties and quasi-varieties of universal algebras.
Descrição
Palavras-chave
Mal'tsev categories Categories Shifting Lemma Congruence modular varieties 3-permutable varieties
Contexto Educativo
Citação
Editora
Springer Basel Ag