Operations on triple cohomology

Abstract

Cohomology operations, such as the cup product and Steenrod squares, are fundamental tools in algebraic topology, and similar constructions are well known for certain algebra types. We here give such a product for algebras defined by a triple over a category of modules, unifying the known examples and extending these to algebras of a most general character. The product is defined on the cochains of the non-homogeneous complex enriched over the category of coalgebras and satisfies a Leibnitz formula.