论文信息 - A New Characterisation of Goursat Categories

A New Characterisation of Goursat Categories

We present a new characterisation of Goursat categories in terms of special kind of pushouts, that we call Goursat pushouts. This allows one to prove that, for a regular category, the Goursat property is actually equivalent to the validity of the denormalised 3-by-3 Lemma. Goursat pushouts are also useful to clarify, from a categorical perspective, the existence of the quaternary operations characterising 3-permutable varieties.

Marino Gran | Diana Rodelo

[1] Marino Gran,et al. A universal construction in Goursat categories , 2008 .

[2] D. Bourn. The denormalized 3×3 lemma , 2003 .

[3] The 3-by-3 lemma for regular Goursat categories , 2004 .

[4] A. Mitschke,et al. Implication algebras are 3-permutable and 3-distributive , 1971 .

[5] Joachim Lambek,et al. Diagram chasing in Mal'cev categories , 1991 .

[6] Dominique Bourn,et al. Mal'cev, Protomodular, Homological and Semi-Abelian Categories , 2004 .

[7] G. M. Kelly,et al. Some remarks on Maltsev and Goursat categories , 1993, Appl. Categorical Struct..

[8] G. M. Kelly,et al. Galois theory and a general notion of central extension , 1994 .

[9] J. Hagemann,et al. Onn-permutable congruences , 1973 .

[10] F. Borceux,et al. On closure operators and reflections in Goursat categories , 2007, 0712.0890.

[11] Valentina Rossi,et al. Admissible Galois Structures and Coverings in Regular Mal’cev Categories , 2006, Appl. Categorical Struct..

[12] Theo Buehler,et al. Exact Categories , 2008, 0811.1480.

[13] George Janelidze,et al. Descent for Regular Epimorphisms in Barr Exact Goursat Categories , 2011, Appl. Categorical Struct..

[14] n-Permutable locally finitely presentable categories , 2020 .