Category:Definitions/Sheaf Theory
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This category contains definitions related to Sheaf Theory.
Related results can be found in Category:Sheaf Theory.
A $\mathbf C$-valued sheaf $\FF$ on $T$ is a $\mathbf C$-valued presheaf such that for all open $U \subseteq S$ and all open covers $\sequence {U_i} _{i \mathop \in I}$ of $U$:
- $\struct {\map \FF U, \paren {\operatorname {res}_{U_i}^U}_{i \mathop \in I} }$
is the limit of the restriction of $\FF$ to the full subcategory of the category of open sets of $T$ with objects $\set U \cup \set {U_i: i \in I} \cup \set {U_i \cap U_j: \tuple {i, j} \in I^2}$.
Subcategories
This category has the following 2 subcategories, out of 2 total.
S
- Definitions/Sheafifications (3 P)
- Definitions/Stacks (5 P)
Pages in category "Definitions/Sheaf Theory"
The following 36 pages are in this category, out of 36 total.
A
C
D
P
S
- Definition:Section of Étalé Space
- Definition:Section of Étalé Space/Definition 1
- Definition:Section of Étalé Space/Definition 2
- Definition:Sheaf Cohomology
- Definition:Sheaf on Topological Space
- Definition:Sheaf on Topological Space/Definition 1
- Definition:Sheaf on Topological Space/Definition 2
- Definition:Sheaf on Topological Space/Definition 3
- Definition:Sheaf on Topological Space/Definition 4
- Definition:Sheafification
- Definition:Stack
- Definition:Stalk of Presheaf