تقرير
Expanding \v{C}ech cohomology for quantales
| العنوان: | Expanding \v{C}ech cohomology for quantales |
|---|---|
| المؤلفون: | Tenório, Ana Luiza, Arndt, Peter, Mariano, Hugo Luiz |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Category Theory, Mathematics - Rings and Algebras, 18F75 55N30 13D03 |
| الوصف: | We expand \v{C}ech cohomology of a topological space $X$ with values in a presheaf on $X$ to \v{C}ech cohomology of a commutative ring with unity $R$ with values in a presheaf on $R$. The strategy is to observe that both the set of open subsets of $X$ and the set of ideals of $R$ provide examples of a (semicartesian) quantale. We study a particular pair of (adjoint) functors $(\theta, \tau)$ between the quantale of open subsets of $X$ and the quantale of ideals of $C(X)$, the ring of real-valued continuous functions on $X$. This leads to the main result of this paper: the $q$th \v{C}ech cohomology groups of $X$ with values on the constant sheaf $F$ on $X$ is isomorphic to the $q$th \v{C}ech cohomology groups of the ring $C(X)$ with values on a sheaf $F \circ \tau$ on $C(X)$. Comment: 26 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.12884 |
| رقم الأكسشن: | edsarx.2404.12884 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |