  Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category.
Given a composition of two commutative squares in $\mathcal{C}$, if two
commutative squares are homotopy cartesian, then their composition is also a
homotopy cartesian. This covers the result by Mac Lane (1998) for abelian
categories and the result by Christensen and Frankland (2022) for triangulated
categories.
