A note on two commutators

• Author(s): Martins-Ferreira, Nelson ; Van der Linden, Tim
• Date: 2009
• Persistent ID: http://hdl.handle.net/10316/13631
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Commutator; Internal re exive graph; Star-multiplication; Groupoid; Protomodular category; Semi-abelian category
• Document Type: Preprint
• Language: English

Description

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.