SAMS Subject Classification Number: 4

Many algebraic categories satisfy the property: given two coequaliser diagrams \(C_1 \rightrightarrows X_1 \rightarrow Y_1\) and \(C_2 \rightrightarrows X_2 \rightarrow Y_2\), their product \(C_1 \times C_2 \rightrightarrows X_1 \times X_2 \rightarrow Y_1 \times Y_2\) is again a coequaliser diagram, i.e., binary products commute with coequalisers. The aim of this talk is to present an algebraic analysis of this property, showing how it may be characterised for general varieties of algebras, as well as showing how it provides a natural setting in which to study Huq-centrality of morphisms. Much of the behaviour of Huq-centrality for unital categories [1] is retained in our setting, including categories which are (weakly) unital, but also categories outside of the unital setting.

[1] D. Bourn, Intrinsic centrality and associated classifying properties, Journal of Algebra 256 (2002), 126–145.