Characterization of protomodular varieties of universal algebras

By Dominique Bourn, George Janelidze. Theory and Applications of Categories, 2003

107 citations recorded by the source corpus.

Protomodular categories were introduced by the first author more than ten years ago. We show that a variety V of universal algebras is protomodular if and only if it has 0-ary terms e1,...,en, binary terms t1,...,tn, and (n+1)-ary term t satisfying the identities t(x,t1(x,y),...,tn(x,y)) = y and ti(x,x )= ei for each i =1 ,...,n.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/23e1c3f0e00cc57dd84d879bbfb0b1cb001b22b1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Marino Gran
2. Tim Van der Linden
3. Sandra Mantovani
4. Giuseppe Metere

In Computational Theory and Mathematics

1. Tim Van der Linden
2. Marino Gran

In Mathematical Physics

1. Tim Van der Linden
2. Marino Gran
3. Sandra Mantovani
4. Giuseppe Metere

Citations in the corpus

• On the representability of actionsin a semi-abelian category (2005, unknown): “models have been characterized in [ 14 ]: they are the theories containing, for some natural number n ∈ N”
• Baer invariants in semi-abelian categories I:General theory (2004, unknown): “Semi-abelian varieties were characterized by Bourn and Janelidze in [11].”
• Baer invariants in semi-abelian categories II: Homology (2004, unknown): “A characterisation of such varieties of algebras over Set is given by Bourn and Janelidze in their paper [13].”
• On the second cohomology group in semi-abelian categories (2005, result): “Such categories were characterized by Gran and Rosický in [26] by extending a previous result due to Bourn and Janelidze [15].”