In this note we show that a finite full subcategory of an hereditary small $\mathbb{Z}$-category is hereditary. As a specialization we obtain the result proved in \cite{le,co.ru}, namely that the endomorphism ring of a finitely generated projective module over an hereditary ring is also hereditary, see also \cite{gahe.gopa}. In particular if $A$ is an hereditary ring and $e$ is an idempotent, the ring $eAe$ is also hereditary.