Isbell共轭与自反完备化
Isbell conjugacy and the reflexive completion
摘要：
范畴的自反完备化由其上的集值函子组成，这些函子与它们的双共轭正则同构。在回顾了这两个建设和Isbell共轭本身，我们给出了新的例子，并回顾了Isbell的主要成果，从1960年在现代范畴的背景下。我们建立了自反完备化是函子的意义，并找到了两个范畴具有等价自反完备化的条件。我们描述了自反完备化和柯西完备化之间的关系，确定了在任意自反完备化中存在哪些极限和共极限，并精确地定义了一个范畴的自反完备化是其上的协变函子和反变函子范畴的交集。
英文摘要：
The reflexive completion of a category consists of the Set-valued functors on it that are canonically isomorphic to their double conjugate. After reviewing both this construction and Isbell conjugacy itself, we give new examples and revisit Isbell's main results from 1960 in a modern categorical context. We establish the sense in which reflexive completion is functorial, and find conditions under which two categories have equivalent reflexive completions. We describe the relationship between the reflexive and Cauchy completions, determine exactly which limits and colimits exist in an arbitrary reflexive completion, and make precise the sense in which the reflexive completion of a category is the intersection of the categories of covariant and contravariant functors on it.
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。
