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Some properties and applications of natural vector bundle morphisms $T_A\circ {⨂}_s^q\to {⨂}_s^q\circ T_A$ over $i{d}_{T_A}$ are presented.

Let $\left(G,\omega \right)$ be a presymplectic groupoid. In this paper we characterize the infinitesimal counter part of the tangent presymplectic groupoid of higher order, $(T^{r}G,{\omega }^{\left(c\right)})$ where $T^{r}G$ is the tangent groupoid of higher order and ${\omega }^{\left(c\right)}$ is the complete lift of higher order of presymplectic form $\omega$.