A note on two commutators

• Autor(es): Martins-Ferreira, Nelson ; Van der Linden, Tim
• Data: 2009
• Identificador Persistente: http://hdl.handle.net/10316/13631
• Origem: Estudo Geral - Universidade de Coimbra
• Assunto(s): Commutator; Internal re exive graph; Star-multiplication; Groupoid; Protomodular category; Semi-abelian category
• Tipo de Documento: Preprint
• Idioma: Inglês

Descrição

We show that two known conditions which naturally arose in commutator theory and in the theory of internal crossed modules coincide: every starmultiplicative graph is multiplicative if and only if every two e ective equivalence relations commute as soon as so do their normalisations. This answers a question asked by George Janelidze.