与拓扑和微分拓扑相关的层范畴的伴随关系
An adjunction of the categories of sheaves related to a topology and a diffeology
浏览论文内容
中文总结 AI 辅助
本文研究微分拓扑空间与拓扑空间间的伴随函子，在二者的层范畴间引入两对函子并阐明其伴随性，且未应用拓扑斯一般理论。
中文摘要 AI 辅助
在微分拓扑空间范畴与拓扑空间范畴之间存在一对伴随函子(D, C)。本文利用这些函子，在微分拓扑空间的层范畴与拓扑空间的层范畴之间引入两对函子。随后阐明，这些新函子的伴随性可由C和D的单位与余单位诱导的函子来刻画。由微分拓扑空间和拓扑空间得到的site之间不存在自然函子，因此，本文在不应用拓扑斯一般理论的情况下，详细阐述了层范畴上的伴随关系。
英文摘要
There exists an adjoint pair (D, C) of functors between the category of diffeological spaces and that of topological spaces. In this article, by using the functors, we introduce two pairs of functors between the categories of sheaves on a diffeological space and on a topological space. Then, the adjointness of the novel functors up to the functors induced by the unit and counit of C and D is clarified. There is no natural functor between sites obtained by a diffeological space and a topological space. Therefore, the adjunctions on the categories of sheaves are elaborated without applying the general theory of topoi.
发表机构
- Shinshu University（信州大学）
机构由 AI 辅助整理，请以论文原文为准。
