The left heart and exact hull of an additive regular category

Quasi-abelian categories are abundant in functional analysis and representation theory. It is known that a quasi-abelian category $\mathcal{E}$ cotilting torsionfree class of an abelian category. In fact, this property characterizes categories. This ambient derived equivalent to the $\mathcal{E}$, can be constructed as heart $\mathcal{LH}(\mathcal{E})$ $t$-structure on bounded $\mathbf{D}^b(\mathcal{E})$ or localization monomorphisms $\mathcal{E}$. However, there natural examples which not quasi-abelian, but merely one-sided even weaker. Examples $\operatorname{LB}$-spaces complete Hausdorff locally convex spaces. paper, we consider additive regular generalization covers aforementioned examples. Additive characterized those subcategories closed under subobjects. As for categories, show such found $\operatorname{t}$-structure $\mathbf{D}^b(\mathcal{E})$, our proof last construction, formulate prove version Auslander's formula Whereas exact way, has structure. Such 2-universally embedded into its hull. We hull again