论文标题
双重访问和双层可容纳2类
Bi-accessible and bipresentable 2-categories
论文作者
论文摘要
我们开发了二维版本的可访问性和与扁平假功能的形式主义兼容的可及性。首先，我们给出了二维典型概念，过滤性和辅助性的不同概念的先决条件。特别是我们表明，出于我们的目的，在实践中，Sigma过滤和分支性实际上是等效的。然后，我们根据双色对象和分叉双晶象来定义双重和可见度的两类。然后，我们将它们描述为平坦的伪造器的类别。我们还证明了一个可访问的右双接合函数定理，并推断出与小比尔（Bilex）2类别的二维Gabriel-ulmer双重性，并有限双层可容忍的2类。最后，我们表明，猫在双期伪内的伪代数的两类是有限的双依性的，特别是捕获了Lex的案例，Lex是小型LEX类别的2类。我们进一步证明，我们援引Lex-Colimits的技术，在分类逻辑（REG，EX，COH，EXT，EXT，ADH，PRITOP）中产生的几个2类也是有限的。
We develop a 2-dimensional version of accessibility and presentability compatible with the formalism of flat pseudofunctors. First we give prerequisites on the different notions of 2-dimensional colimits, filteredness and cofinality; in particular we show that sigma-filteredness and bifilteredness are actually equivalent in practice for our purposes. Then, we define bi-accessible and bipresentable 2-categories in terms of bicompact objects and bifiltered bicolimits. We then characterize them as categories of flat pseudofunctors. We also prove a bi-accessible right bi-adjoint functor theorem and deduce a 2-dimensional Gabriel-Ulmer duality relating small bilex 2-categories and finitely bipresentable 2-categories. Finally, we show that 2-categories of pseudo-algebras of bifinitary pseudomonads on Cat are finitely bipresentable, which in particular captures the case of Lex, the 2-category of small lex categories. Invoking the technology of lex-colimits, we prove further that several 2-categories arising in categorical logic (Reg, Ex, Coh, Ext, Adh, Pretop) are also finitely bipresentable.
