分支、补集和反射公式
Components, complements and reflection formulas
摘要：
研究了在基范畴X上同时包含离散纤维化和离散光学纤维化的基本性质。特别是，我们举例说明了公式（|P）x = ten（x/X，P）;（P|）x = hom（X/x，P），给出反射|P和共反射P|在离散纤维化中的P/X范畴。显式使用“张量函子“ten：= \comp（- \times -）：Cat/X \times Cat/X \to由乘积的分量给出的集合，允许在二值上下文中对相应的分析进行广泛的推广。对于任意的df A，函子ten（A，-）：Cat/X \to Set有一个右伴随\neg A，其值为dof's（反之亦然）;这样的补算子，在二值情况下，它可以简化为偏序集上下部分之间的经典补，在集值上下文中也是一个有效的工具。各种应用的公式和相应的概念框架。
英文摘要：
Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations in categories over a base category X are considered. In particular, we illustrate the formulas (|P)x = ten(x/X,P) ; (P|)x = hom(X/x,P) which give the reflection |P and the coreflection P| of a category P over X in discrete fibrations. The explicit use of the "tensor functor" ten := \comp(- \times -) : Cat/X \times Cat/X \to Set given by the components of products, allows a vast generalization of the corresponding analysis in the two-valued context. For any df A, the functor ten(A,-) : Cat/X \to Set has a right adjoint \neg A valued in dof's (and vice versa); such a complement operator, which in the two-valued case reduces to the classical complementation between lower and upper parts of a poset, turns out to be an effective tool in the set-valued context as well. Various applications of the formulas and of the accompanying conceptual frame are presented.
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