充实于quantaloid的伴随函子的不动点
Fixed points of adjoint functors enriched in a quantaloid
摘要：
本文建立了在一个小量子面上的范畴间伴随函子的不动点的表示定理。这些结果为形式概念分析和粗糙集理论中概念格的表示定理建立了一个通用的框架，不仅将形式背景的研究领域扩展到了多类型多值背景，而且为构造各种表示定理提供了一种通用的方法.除了将几个著名的表示定理FCA和ESTA，以及制定新的，它表明，在ESTA的概念格总是可以表示为FCA通过相对伪补的给定的情况下，特别是如果上下文值在一个非Girard quantaloid。
英文摘要：
Representation theorems are established for fixed points of adjoint functors between categories enriched in a small quantaloid. In a very general setting these results set up a common framework for representation theorems of concept lattices in formal concept analysis (FCA) and rough set theory (RST), which not only extend the realm of formal contexts to multi-typed and multi-valued ones, but also provide a general approach to construct various kinds of representation theorems. Besides incorporating several well-known representation theorems in FCA and RST as well as formulating new ones, it is shown that concept lattices in RST can always be represented as those in FCA through relative pseudo-complements of the given contexts, especially if the contexts are valued in a non-Girard quantaloid.
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