Connected limits, familial representability and Artin glueing
Connected limits, familial representability and Artin glueing
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关联限制、家族代表性和 Artin 粘合
DOI：
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发表时间：
1995
影响因子：
0.5
通讯作者：
P. Johnstone
中科院分区：
文献类型：
--
作者：
A. Carboni;P. Johnstone
我们考虑函子F从预层拓扑到集合范畴的两个性质：（a）F保持连通极限，（B）F的Artin胶合又是预层拓扑.我们证明了这两个性质实际上是等价的。在这个过程中，我们开发了一个通用的技术相关联的范畴性质的范畴通过阿廷胶合保存性质的函子沿着胶合发生。我们还给出了Set上函子部分具有上述性质，单位和乘法是Carnival自然变换的单子的一个句法刻画。
We consider the following two properties of a functor F from a presheaf topos to the category of sets: (a) F preserves connected limits, and (b) the Artin glueing of F is again a presheaf topos. We show that these two properties are in fact equivalent. In the process, we develop a general technique for associating categorical properties of a category obtained by Artin glueing with preservation properties of the functor along which the glueing takes place. We also give a syntactic characterization of those monads on Set whose functor parts have the above properties, and whose units and multiplications are cartesian natural transformations.