论文标题
Artin胶合胶作为伴随分开扩展
Artin glueings of toposes as adjoint split extensions
论文作者
论文摘要
框架的Artin胶合物对应于框架类别和有限摄影图的伴随分开扩展。我们将这些想法扩展到座椅的设置，并表明，在两类座椅，有限限制的宽度函数和自然变换中，座椅上的Artin胶水对应于伴随分裂扩展的两类概念。引入了这些分裂扩展之间的形态概念，这允许构建类别Ext（H，N）类别。我们表明，Ext（H，N）违反了HOM（H，N），并且可以扩展到HOM 2-函数与自然定义的EXT 2函数之间的2-自然逆向等效性。
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.
