双范畴幂等完备化
Bicategorical Idempotent Completion
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中文总结 AI 辅助
本文在双范畴中严格定义幂等完备化，并证明其与Lawvere意义下的局部幂等完备双范畴的Cauchy完备化一致，为数学物理中的范畴化结构提供理论基础。
中文摘要 AI 辅助
近年来，幂等元的高阶范畴变体已成为研究对象。值得注意的是，它们在由数学物理驱动的代数结构范畴化中出现。在双范畴的背景下，我们给出了Gaiotto和Johnson-Freyd在arXiv:1905.09566中概述的双范畴幂等完备化的严格定义。我们证明了这与Lawvere意义下的局部幂等完备双范畴的Cauchy完备化一致。
英文摘要
In recent years, higher categorical variants of idempotents have become an object of interest. Notably, they appear when categorifying algebraic structures motivated by mathematical physics. Working in the setting of bicategories, we give a rigorous definition of the bicategorical idempotent completion as outlined by Gaiotto and Johnson-Freyd in arXiv:1905.09566. We show that this agrees with the Cauchy completion of a locally idempotent complete bicategory in the sense of Lawvere.
