We know if $C$ is an ordinary additive category, then the addition of maps $f,g:x \rightarrow y$ coincides with the composition

 $$x \xrightarrow{\bigtriangleup} x \oplus x \xrightarrow{(f,g)} y \oplus y \xrightarrow{\bigtriangledown} y,$$

which first and last maps are diagonal and codiagonal maps respectively. This map defines an abelian group structure on $\operatorname{Map}_C(x,y)$.

Now, here is my main question! if $C$ is an additive $\infty$-category, how can we show this operation (on $\operatorname{Map}_C(x,y)$) is commutative and associative up to coherent homotopy? How can we actually show it is commutative and associative up to just homotopy?