A new characterization of Goursat categories

• Author(s): Gran, Marino ; Rodelo, Diana
• Date: 2010
• Persistent ID: http://hdl.handle.net/10316/13706
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Goursat category; 3-by-3 Lemma; Pushouts; Mal'tsev condition
• Document Type: Preprint
• Language: English

Description

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