Homotopical perspective on statistical quantities

We introduce the notion of cumulants as applied to linear maps between associative (or commutative) algebras that are not compatible with algebraic product structure. These have a close relationship $$A_{\infty }$$ and $$C_{\infty morphisms, which classical homotopical tools for analyzing deformations algebraically maps. look at these two different perspectives understand how infinity-morphisms might inform our understanding cumulants. show in presence an or morphism, relevant strongly homotopic zero.