2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140258This unpublished note contains some materials taken from my old study note on groupoids and small categories. It contains a proof for the fact that any groupoid is a group bundle over an equivalence relation. Moreover, the action of a category $G$ on a category $H$ as well as the resulting semi-direct product category $H\times_αG$ will be defined (when either $G$ is a groupoid or $H^{(0)} = G^{(0)}$). If both $G$ and $H$ are groupoids, then $H\times_αG$ is also a groupoid. The reason of producing this note is for people who want to check some details in a recent work of Li.6 pages, unpublished noteCategory TheoryDynamical Systemstext