标题： 纤维方法在二范畴的格兰迪精确性中的应用 显示英文标题

标题： Fibrational approach to Grandis exactness for 2-categories

摘要： 在阿贝尔范畴中，子对象的（双）纤维化与商对象的（双）纤维化同构。 这一性质捕捉了范畴精确结构的重要信息。 事实上，正如第二作者和T.~Weighill所展示的，装备了适当因子系统且子对象的op纤维化相对于该因子系统同构于相对商对象的纤维化的范畴，恰好是Grandis正合范畴。 受到第二作者与Ülo Reimaa正在进行的工作的启发，该工作表明2-范畴中的阿贝尔范畴（选择合适的态射）满足某些二维正合性条件，本文提出了一种Grandis正合范畴的二维概念。 我们通过刻画M.~Dupont和E.~Vitale意义下2-范畴上的那些$(1,1)$-恰当因子系统来达到这一定义，对于这些因子系统，相对2-子对象的弱2-op纤维化与相对2-商对象的弱2-纤维化是双等价的。 显示英文摘要

摘要： In an abelian category, the (bi)fibration of subobjects is isomorphic to the (bi)fibration of quotients. This property captures a substantial information about the exactness structure of a category. Indeed, as it was shown by the second author and T.~Weighill, categories equipped with a proper factorization system such that the opfibration of subobjects relative to the factorization system is isomorphic to the fibration of relative quotients are precisely the Grandis exact categories. Motivated by on-going work of the second author with \"Ulo Reimaa, indicating that the 2-category of abelian categories (with suitably chosen morphisms) satisfies some 2-dimensional exactness conditions, in this paper we propose a 2-dimensional notion of a Grandis exact category. We reach such definition as an outcome of characterizing those $(1,1)$-proper factorization systems on a 2-category in the sense of M.~Dupont and E.~Vitale, for which the weak 2-opfibration of relative 2-subobjects is biequivalent to the weak 2-fibration of relative 2-quotients.