PlanetPhysics/Hereditary Category

Let $𝒞$ be a locally small $𝒜b3$-category. A subcategory $𝒜$ of $𝒞$ is called hereditary if it verifies the following condition: if $Y$ is an [[../TrivialGroupoid/|object]] in a full subcategory $ℱ$ of $𝒞$, then any subobject of $Y$ is also in $ℱ$.