从Dedekind-MacNeille到Lambek-Isbell的严格限制和完成
Tight limits and completions from Dedekind-MacNeille to Lambek-Isbell
摘要：
虽然偏序集中的任何下确界也可以计算为上确界，反之亦然，但范畴极限和上极限并不总是彼此近似。如果我从下面接近一个点，而你从上面接近它，那么如果我们生活在偏序集中，我们肯定会相遇，但我们可能在一个范畴中错过对方。我们能描述极限和上极限的特征吗？它们彼此近似，并保证满足？这样的极限和共极限被称为“紧”。一些至关重要的网络应用程序依赖于它们。本文刻画了紧极限和余极限，并描述了紧完备化，它是通过将核结构应用于松散完备化之间的交换而得到的。正如偏序集的Dedekind-MacNeille完备化保持任何存在的下确界和上确界，范畴的紧完备化保持任何存在的紧极限和上极限，因此是幂等的。
英文摘要：
While any infimum in a poset can also be computed as a supremum, and vice versa, categorical limits and colimits do not always approximate each other. If I approach a point from below, and you approach it from above, then we will surely meet if we live in a poset, but we may miss each other in a category. Can we characterize the limits and the colimits that approximate each other, and guarantee that we will meet? Such limits and colimits are called *tight*. Some critically important network applications depend on them. This paper characterizes tight limits and colimits, and describes tight completions, derived by applying the nucleus construction to adjunctions between loose completions. Just as the Dedekind-MacNeille completion of a poset preserves any existing infima and suprema, the tight completion of a category preserves any existing tight limits and colimits and is therefore idempotent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
