hereditary category

Definition 0.1   Let $ \mathcal{C}$ be a locally small $ \mathcal{A}b3$ -category. A subcategory $ \mathcal{A}$ of $ \mathcal{C}$ is called hereditary if it verifies the following condition: if $ Y$ is an object in a full subcategory $ \mathcal{F}$ of $ \mathcal{C}$ , then any subobject of $ Y$ is also in $ \mathcal{F}$ .



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