Categorical chain conditions for Étale groupoid algebras

Let R be a unital commutative ring and G an ample groupoid. Using the topology of the groupoid G, Steinberg defined an étale groupoid algebra RG. These étale groupoid algebras generalize various algebras including group algebras, commutative algebras over a field generated by idempotents, traditional groupoid algebras, Leavitt path algebras, higher-rank graph algebras, and inverse semigroup algebras. Steinberg later characterized the classical chain conditions for étale groupoid algebras. We characterize categorically noetherian and artinian, locally noetherian and artinian, and semisimple étale groupoid algebras, generalizing existing results for Leavitt path algebras and introducing new results for inverse semigroup algebras.