Heaps of modules: homological aspects

The definitions of projective objects and Gorenstein projective objects in the category of heaps of $T$-modules are posed, where $T$ is a truss. It is shown that a heap of $T$-modules $P$ is projective if and only if $\mathcal{G}_{e_p}(P)$ is a projective $R(T)$-module for all $e_p\in P$ and a heap