A tripos based on compact Hausdorff spaces
英文摘要:
The category of compact Hausdorff spaces is the base of tripos. As such it can be freely completed to an elementary topos.
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Fabio Pasquali
The category of compact Hausdorff spaces is the base of tripos. As such it can be freely completed to an elementary topos.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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We prove that for any small category $\mathcal{C}$, the category $\mathbf{KHausLoc}_{\hat{\mathcal{C}}}$ of compact Hausdorff locales in the presheaf topos $\hat{\mathcal{C}}$, is equivalent to the category of functors $\mathcal{C} \to \mathbf{KHausLoc}$.
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Barr-coexactness for metric compact Hausdorff spaces
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A condensed set is a sheaf on the site of Stone spaces and continuous maps. We prove that condensed sets are equivalent to sheaves on the site of compact Hausdorff spaces and continuous maps. As an application, we show that there exists a model structure on the category of condensed sets.
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本文针对紧豪斯多夫空间范畴的对偶非有限共 concrete 的结论,给出了简短拓扑证明,并通过识别特定序列余极限进一步强化了该结果。
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本文证明了将局部紧 Hausdorff 空间映射到谱层 $\infty$-范畴的函子是连续六函子形式体系的初始对象,并将 Efimov 的代数 $K$-理论计算推广至所有局部化不变量。
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该研究将显式离散、紧豪斯多夫的拟波兰空间范畴构造为有效拟波兰空间与可计算映射范畴的内部范畴,且证明斯通对偶性可计算,为相关拓扑范畴的可计算性研究提供了基础。
Extending the Stone Duality Theorem, we prove two duality theorems for the category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. Both of them imply easily the Tarski Duality Theorem, as well as two new duality theorems for the category EDTych of extremally disconnected Tychonoff spaces and continuous maps. Also, we describe two categories which are dually equivalent to the category ZComp of zero-dimensional Hausdorff compactifications of zero-dimensional Hausdorff spaces and obtain as a corollary the Dwinger Theorem about zero-dimensional compactifications of a zero-dimensio…
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In 1962, H. de Vries proved a duality theorem for the category {\bf HC} of compact Hausdorff spaces and continuous maps. The composition of the morphisms of the dual category obtained by him differs from the set-theoretic one. Here we obtain a new category dual to the category {\bf HLC} of locally compact Hausdorff spaces and continuous maps for which the composition of the morphisms is a natural one but the morphisms are multi-valued maps.
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