We use the notion of universal extension in a linear abelian category to study extensions of variations of mixed Hodge structure and convergent and overconvergent isocrystals. The results we obtain apply, for example, to prove the exactness of some homotopy sequences for these categories and to study $F$-able isocrystals.

中文翻译：

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论坦纳基语范畴的普遍扩展

我们使用线性阿贝尔范畴中的普遍扩展的概念来研究混合霍奇结构和收敛和过收敛等晶的变化的扩展。例如，我们获得的结果适用于证明这些类别的某些同伦序列的准确性并研究$F$-able 等晶。