双范畴、双等价与双可解释性
Bicategories, Biequivalence, and Bi-Interpretability
AI总结：
本文通过构造相干理论双范畴与相干范畴双范畴之间的双等价，给出双可解释性的范畴刻画，并利用正合完备化得到两个理论双可解释的充要条件，推广到一阶逻辑常见片段。
摘要：
我们明确了一阶相干逻辑中语法与语法范畴之间的对应关系，给出了双可解释性的范畴刻画。具体做法是在相干理论的双范畴与相干范畴的（严格）双范畴之间构造一个双等价。该双等价涉及更强的保持相等的双可解释性，我们利用它，通过关联各理论语法范畴的正合完备化，得到了两个理论一般地双可解释的充分必要条件。这些结果可类似地推广到一阶逻辑的常见片段，从而澄清了逻辑语法与语法范畴之间长期以来被直觉感知的关系。
英文摘要：
We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of coherent theories and the (strict) bicategory of coherent categories. While the biequivalence concerns the stronger equality-preserving bi-interpretability, we use it to obtain a necessary and sufficient condition for two theories to be bi-interpretable in general, by relating the exact completions of their syntactic categories. These results extend analogously to familiar fragments of first-order logic, thereby clarifying the long-intuited relation between logical syntax and syntactic categories.
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。
