Grothendieck拓扑的局部右双伴、双稳态伪函子和2-几何
Local right biadjoints, bistable pseudofunctors and 2-geometries for Grothendieck topoi
摘要：
我们提供了双范畴的类似物的几个方面的概念的几何理论的意义上的频谱。首先引入局部右双伴随的概念，证明了它与双稳态伪函子的等价性，并对一个类似的1-范畴结果进行了范畴化。我们还描述了进一步宽松的条件，给出了一些性质已经知道宽松的家族pseudofunctors。我们还描述了2维的正交性和因式分解系统的类似物，并使用它们来构造通过包含左对象和左映射的双稳态伪函子的例子。我们将后者的建设几个例子的因式分解系统的几何态射产生几何Grothendieck拓扑的情况。特别是，我们证明了一个新的（终端连接，pro-etale）分解定理的几何态射，这对应于一定的局部几何参与一般建设的频谱。
英文摘要：
We provide bicategorical analogs of several aspects of the notion of geometry in the sense of the theory of spectrum. We first introduce a notion of local right biadjoint, and prove it to be equivalent to a notion of bistable pseudofunctor, categorifying an analog 1-categorical result. We also describe further laxness conditions, giving some properties of the already known lax familial pseudofunctors. We also describe 2-dimensional analogs of orthogonality and factorization systems, and use them to construct examples of bistable pseudofunctors through inclusion of left objects and left maps. We apply the latter construction to several examples of factorization systems for geometric morphisms to produce geometry-like situations for Grothendieck topoi. In particular we prove a new (terminally connected, pro-etale) factorization theorem for geometric morphisms, which corresponds to a certain local geometry involved in the general construction of spectra.
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