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Stratified categorical fixed-basis fuzzy topological spaces and their duality

机译：分层分类固定基模糊拓扑空间及其对偶

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摘要

For an abstract category C, a class M of C-monomorphisms and a fixed C-object L, we introduce stratified C-M-L-spaces to be categorical counterparts of stratified fixed-basis fuzzy topological spaces in C, and consider their category SC-M-L-Top. As two main results of this paper, it is shown that SC-M-L-Top is dually adjoint to the comma category L down arrow C, and this adjunction can be restricted to a dual equivalence between the full category of L down arrow C with comma-spatial objects and the full category of SC-M-L-Top with comma-sober objects. The present paper also describes applications and relationships of these results to stratified fixed-basis fuzzy topological spaces. In this respect, a considerable part of this paper is devoted to stratified L-quasi-topological spaces and their duality. (C) 2014 Elsevier B.V. All rights reserved.
机译：对于抽象类别C，C单态类M和固定C对象L，我们引入分层CML空间作为C中分层固定基础模糊拓扑空间的分类对应物，并考虑其类别SC-ML-最佳。作为本文的两个主要结果，表明SC-ML-Top与逗号类别L向下箭头C双重对接，并且该附加词可以限制为L向下箭头C的完整类别与逗号之间的对等对等-空间对象以及SC-ML-Top的完整类别以及逗号清醒的对象。本文还描述了这些结果在分层固定基模糊拓扑空间中的应用及其关系。在这方面，本文的相当一部分致力于分层的L-拟拓扑空间及其对偶性。 （C）2014 Elsevier B.V.保留所有权利。

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