Algebraic coalitions (Q1272132)

An algebra \(A\) is called abelian whenever the centre of \(A\) is equal to \(A\times A\). {SELF} denotes the category of all graphs \(\mathcal R\) that have exactly one object \(0_{\mathcal R}\), together with all graph maps between any two such graphs. The idea of an algebra in {SELF} is introduced in the paper. It is shown that such algebras are abelian with a one-element subalgebra in a congruence modular variety. This leads to the notion of algebraic coalition, which is characterized for congruence modular varieties and for varieties of Jónsson-Tarski algebras. Finally, the relationship among algebraic coalitions, Gumm difference term, and the centre of an algebra is studied.