Homotopy methods in absolute valued structures theory

We introduce homotopical techniques in the frameworks of two-graded absolute valued algebras and absolute valued triple systems, which will simplify the study of these structures. To this end, we previously refine and concrete the known descriptions of two-graded absolute valued algebras and absolute valued triple systems, as well as characterize the fact that an absolute valued triple system is the odd part of an absolute valued two-graded algebra.