Coalgebraic approach to the Loday infinity category, stem differential for \(2n\)-ary graded and homotopy algebras (Q968265)

This paper introduces a graded twisted-coassociative coproduct on the tensor algebra of a graded vector space. The authors start by studying the properties of cohomology algebras and by recalling the relevant notions and facts. A definition of a Zinbiel coalgebra structure is also given. The authors investigate then Loday infinity quasi-isomorphisms and prove a minimal model theorem for Loday infinity algebras. The graded Lie bracket of coderivations gives rise to a graded Lie stem bracket on the cochain spaces of graded Loday, Loday infinity and \(2n\)-ary graded Loday algebras. These graded Loday algebras are special strongly homotopy Loday algebras.