Toposes的Artin glueings作为伴随分裂扩张
Artin glueings of toposes as adjoint split extensions
AI总结：
本文将frames的Artin glueings与伴随分裂扩张的对应关系扩展至toposes的2-范畴，证明其构成2-自然反变等价，并引入态射构造了范畴Ext(H,N)。
摘要：
frames的Artin glueings对应于frames及保有限交映射范畴中的伴随分裂扩张。我们将这些思想扩展到toposes的设定中，并证明toposes的Artin glueings对应于toposes、保有限极限函子与自然变换的2-范畴中伴随分裂扩张的2-范畴概念。引入了这些分裂扩张之间的态射概念，从而允许构造范畴Ext(H,N)。我们证明Ext(H,N)反变等价于Hom(H,N)，而且这可以扩展为Hom 2-函子与自然定义的Ext 2-函子之间的2-自然反变等价。
英文摘要：
Artin glueings of frames correspond to adjoint split extensions in the category of frames and finite-meet-preserving maps. We extend these ideas to the setting of toposes and show that Artin glueings of toposes correspond to a 2-categorical notion of adjoint split extensions in the 2-category of toposes, finite-limit-preserving functors and natural transformations. A notion of morphism between these split extensions is introduced, which allows the category Ext(H,N) to be constructed. We show that Ext(H,N) is contravariantly equivalent to Hom(H,N), and moreover, that this can be extended to a 2-natural contravariant equivalence between the Hom 2-functor and a naturally defined Ext 2-functor.
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。
