波兰群范畴的正合完备化
The Exact Completion of the Category of Polish Groups
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中文总结 AI 辅助
本文研究波兰群范畴的正合完备化，将其刻画为具有波兰覆盖且配备博雷尔可定义群同态的群范畴，同时给出该正合完备化态射的等价刻画及相关子范畴的对应描述。
中文摘要 AI 辅助
本文证明，波兰群与连续群同态构成的同调范畴作为正则范畴的正合完备化，是具有波兰覆盖且配备博雷尔可定义群同态的群范畴；我们还得到该正合完备化中态射的若干等价刻画，并推导出波兰群范畴多个重要子范畴的类似描述。
英文摘要
This article shows that the exact completion as a regular category of the homological category of Polish groups and continuous group homomorphisms is the category of groups with a Polish cover and Borel-definable group homomorphisms. We also obtain several equivalent characterizations for the morphisms in the exact completion. An analogous description is deduced for several important subcategories of the category of Polish groups.
