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تسجيل مستخدم جديدOn the obscure axiom for one-sided exact categories
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One-sided exact categories are obtained via a weakening of a Quillen exact category. Such one-sided exact categories are homologically similar to Quillen exact categories: a one-sided exact category $mathcal{E}$ can be (essentially uniquely) embedded into its exact hull ${mathcal{E}}^{textrm{ex}}$; this embedding induces a derived equivalence $textbf{D}^b(mathcal{E}) to textbf{D}^b({mathcal{E}}^{textrm{ex}})$. Whereas it is well known that Quillens obscure axioms are redundant for exact categories, some one-sided exact categories are known to not satisfy the corresponding obscure axiom. In fact, we show that the failure of the obscure axiom is controlled by the embedding of $mathcal{E}$ into its exact hull ${mathcal{E}}^{textrm{ex}}.$ In this paper, we introduce thr
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In this paper, we introduce quotients of exact categories by percolating subcategories. This approach extends earlier localization theories by Cardenas and Schlichting for exact categories, allowing new examples. Let $mathcal{A}$ be a percolating sub
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We consider the quotient of an exact or one-sided exact category $mathcal{E}$ by a so-called percolating subcategory $mathcal{A}$. For exact categories, such a quotient is constructed in two steps. Firstly, one localizes $mathcal{E}$ at a suitable cl
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