AI 中文总结
本文研究格罗滕迪克范畴中的卡普兰斯基类，提出一致平稳卡普兰斯基类概念，证明这类类虽通常无预覆盖但常满足模型论稳定性，举例说明相关类在纯嵌入下的稳定性。
AI 中文摘要
2000年左右平坦覆盖猜想被证明后不久，格罗滕迪克范畴的类中引入了两个相关概念：可解构类和严格更弱的卡普兰斯基类。所有常用的卡普兰斯基类，如$R$-模范畴中平坦Mittag-Leffler模的类$\boldsymbol{\text{FM}}$，以及拟凝聚层范畴中Drinfeld向量丛的类$\boldsymbol{\text{D}}$，都满足本文引入的更强性质：它们是一致平稳卡普兰斯基类。这类类通常缺乏使可解构类成为现代相对同调代数核心的关键特性（预覆盖的存在性），但常足以支撑模型论稳定性，即使在没有融合性质、存在各种受限态射类，以及某些非加性环境中也成立。例如，带纯嵌入的$\boldsymbol{\text{FM}}$，以及带（范畴或几何）纯嵌入的$\boldsymbol{\text{D}}$，在所有足够大的基数下都是稳定的。
英文摘要
Soon after the proof of the Flat Cover Conjecture around the year 2000, two related concepts were introduced for classes in Grothendieck categories: \emph{Deconstructible classes} and the strictly weaker \emph{Kaplansky classes}. All commonly-studied Kaplansky classes, such as the class $\mathcal{FM}$ of Flat Mittag-Leffler modules in $R$-Mod and the class $\mathcal{D}$ of Drinfeld vector bundles in Qcoh($X$), satisfy a stronger property we introduce here: they are \emph{Uniformly Stationary Kaplansky} classes. While such classes generally lack the key feature (existence of precovers) that make deconstructible classes so central to modern relative homological algebra, they often suffice for model-theoretic stability. This is true even in the absence of the Amalgamation Property, with various restricted classes of morphisms, and in some non-additive settings. For example, $\mathcal{FM}$ with pure embeddings, and $\mathcal{D}$ with (either categorical or geometric) pure embeddings, are stable in all sufficiently closed cardinals.
