given an $r$-uniform hypergraph $\mathcal{a} \subset x^{(r)}$, the (lower) shadow of $\mathcal{a}$, denoted $\delta(\mathcal{a})$ is defined as $\delta(\mathcal{a}):= \{ b \in x^{(r-1)} : b \subset a \text{ for some } a \in \mathcal{a} \}$. in this talk, we will explore the classical kruskal-katona theorem which gives a lower bound on $|\delta(\mathcal{a})|$ and describe related notions of colex order and compression operators on set families.