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Let $(\mathcal{A},\mathcal{E})$ be an exact category. We establish basicresults that allow one to identify sub(bi)functors of$\operatorname{Ext}_{\mathcal{E}}(-,-)$ using additivity of numerical functionsand restriction to subcategories. We also study a small number of these newfunctors over commutative local rings in details, and find a range ofapplications from detecting regularity to understanding Ulrich modules.

Exact subcategories, subfunctors of $\operatorname{Ext}$, and some applications