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

我们介绍了累积量的概念，该概念适用于与代数乘积结构不兼容的关联（或可交换）代数之间的线性映射。这些累积量与\（A _ {\ infty} \）和\（C _ {\ infty} \）态素有着密切的关系，它们是用于分析代数兼容线性图变形的经典同位工具。我们从这两种不同的观点出发，以了解无穷形态可以如何帮助我们理解累积量。我们表明，在存在\（A _ {\ infty} \）或\（C _ {\ infty} \）态射的情况下，相关累积量与零的同位性很强。