We demonstrate equivalence between two definitions of lower finite highest weight categories. We also show that, in the presence of a duality, a lower finite highest weight structure on a category is unique. Finally, we give a new proof for the fact that any abelian category is extension full in its ind-completion.

中文翻译：

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ind-completions 和最高权重类别的一些同源属性

我们证明了较低有限最高权重类别的两个定义之间的等效性。我们还表明，在存在二元性的情况下，类别上较低的有限最高权重结构是唯一的。最后，我们给出了一个新的证明，即任何阿贝尔范畴在其 ind-completion 中都是满拓的。