sheaf
collection of objects associated to subsets of a space in a manner admitting gluing and restriction
| rdfs:label |
"sheaf"@en
|
|
skos:alt |
"fai"@ast
"fexes"@ast
|
| schema:description |
"collection of objects associated to subsets of a space in a manner admitting gluing and restriction"@en
|
|
schema:date |
"2026-10-06T09:31:44+00:00"^^xsd:dateTime |
| schema:version | 2553848196 |
| wikibase:identifiers | 14 |
| wikibase:sitelinks | 30 |
| wikibase:statements | 27 |
| p:P10283 | wd:statement/Q595298-CB38833B-1AAA-45A0-BF93-7F31AA7C0BD3 |
| p:P13591 | wd:statement/Q595298-C0879C7D-82A1-46CE-B2FE-89BD936D5883 |
| p:P1417 | wd:statement/Q595298-10FD220F-646C-455D-A5B0-1D4C9CD5A01E |
| p:P14540 | wd:statement/Q595298-DDE7234F-9691-4DF2-BBC2-465EF0DDC9C1 |
| p:P1552 | wd:statement/Q595298-39342c71-455e-ad01-4c2a-ed6051cbb8eb |
| wd:statement/Q595298-4515193d-4ec4-4d0a-088a-f91e0f7d7a62 | |
| wd:statement/Q595298-f3fdd71a-4bc6-d18b-8b43-3f5b03a449c3 | |
| p:P1889 | wd:statement/Q595298-2cd7a1ea-4ebd-1f96-cb96-4a68ae600579 |
| p:P244 | wd:statement/Q595298-B07605CF-8BC5-4289-B69A-C1A70064B1AC |
| p:P2534 | wd:statement/Q595298-1da12004-411e-540b-b724-054ba4f793c6 |
| p:P2579 | wd:statement/Q595298-e777e5d4-4d3b-49b9-6b60-d6a8db236b2e |
| p:P279 | wd:statement/Q595298-2711aa2e-4056-1818-78c4-a8e0cc4482fa |
| wd:statement/Q595298-cb26c82b-42a3-f2ff-f38a-a085315fd23a | |
| p:P2812 | wd:statement/Q595298-7F00E45A-773E-4CB1-8FC6-54698DE00BC0 |
| p:P4215 | wd:statement/Q595298-2b5fe0dc-4e95-cd60-978e-7b111b7667d4 |
| p:P5008 | wd:statement/Q595298-05550735-478A-4713-95C3-21A51CB8E0F2 |
| p:P575 | wd:statement/Q595298-f95e328f-431b-9f77-c2b2-8cb3601eb897 |
| p:P61 | wd:statement/Q595298-2ffa5cc2-4d81-1ea5-373b-357fb5dbf466 |
| p:P6104 | wd:statement/Q595298-00479D5D-9D82-4D1C-985B-B296B73F853B |
| p:P6366 | wd:statement/Q595298-45E8A5C5-2DEE-47FA-B427-1C904D9A7A2B |
| wd:statement/Q595298-687D24D7-CA6D-4FD7-A27B-B308539A37FB | |
| p:P646 | wd:statement/Q595298-4E89ADEC-66A8-45AB-8CB7-BB9B7B8294B1 |
| p:P6781 | wd:statement/Q595298-8d223668-4f59-52c4-749d-a794e7ea1a9d |
| p:P7554 | wd:statement/Q595298-6de5bc1e-43b2-a7d3-8a41-9c9016b86f93 |
| p:P7726 | wd:statement/Q595298-433089d2-436e-843b-9724-fafdddba255b |
| wd:statement/Q595298-f6caba8c-4c83-4517-0026-6018280ce7bb | |
| p:P8189 | wd:statement/Q595298-BE57C516-BAB7-4AC7-A5A9-88E7EF153B0A |
|
p:direct- |
<http:/ |
|
p:direct- |
<https:/ |
|
<https:/ |
|
| wdt:P10283 | "C4017995" |
| wdt:P13591 | "concept/e47d9776-db89-4bc4-8c03-66c3f9f22eb0" |
| wdt:P1417 | "topic/sheaf" |
| wdt:P14540 | cosheaf |
| wdt:P1552 | stalk |
| gluing axiom | |
| global section | |
| wdt:P1889 | sheaf |
| wdt:P244 | "sh85121203" |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>F</mi><mo stretchy="false">:</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">O</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">n</mi></mrow><mo stretchy="false">(</mo><mi>X</mi><msup><mo stretchy="false">)</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi></mrow></mrow></msup><mo stretchy="false" accent="false">→</mo><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">S</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>U</mi><mo stretchy="false">=</mo><munder><mo stretchy="false">⋃</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo stretchy="false">∈</mo><mi>I</mi></mrow></mrow></munder><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">∧</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo stretchy="false">∈</mo><mi>F</mi><mo stretchy="false">(</mo><mi>U</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mo stretchy="false">(</mo><mi mathvariant="normal">∀</mi><mi>i</mi><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">:</mo><mi>s</mi><mo stretchy="false">↾</mo><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">=</mo><mi>t</mi><mo stretchy="false">↾</mo><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi>s</mi><mo stretchy="false">=</mo><mi>t</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi>U</mi><mo stretchy="false">=</mo><munder><mo stretchy="false">⋃</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo stretchy="false">∈</mo><mi>I</mi></mrow></mrow></munder><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">∧</mo><mi mathvariant="normal">∀</mi><mi>i</mi><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">:</mo><msub><mi>s</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">∈</mo><mi>F</mi><mo stretchy="false">(</mo><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi mathvariant="normal">∀</mi><mi>i</mi><mo>,</mo><mi>j</mi><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">:</mo><msub><mi>s</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">↾</mo><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">∩</mo><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo stretchy="false">=</mo><msub><mi>s</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo stretchy="false">↾</mo><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">∩</mo><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi mathvariant="normal">∃</mi><mi>s</mi><mo stretchy="false">∈</mo><mi>F</mi><mo stretchy="false">(</mo><mi>U</mi><mo stretchy="false">)</mo><mi mathvariant="normal">∀</mi><mi>i</mi><mo stretchy="false">∈</mo><mi>I</mi><mo stretchy="false">:</mo><msub><mi>s</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">=</mo><mi>s</mi><mo stretchy="false">↾</mo><msub><mi>U</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | sheaf theory |
| wdt:P279 | presheaf |
| stack | |
| wdt:P2812 | "Sheaf" |
| wdt:P4215 | "sheaf" |
| wdt:P5008 | Wikipedia:Vital articles/Level/4 |
| wdt:P575 | "1947-01-01T00:00:00+00:00"^^xsd:dateTime |
| wdt:P61 | Jean Leray |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "118497674" |
| "4017995" | |
| wdt:P646 | "/m/01kjmy" |
| wdt:P6781 | "Definition:Sheaf_on_Topological_Space" |
| wdt:P7554 | "Sheaf" |
| wdt:P7726 | "Sheaf" |
| "Sheaf1" | |
| wdt:P8189 | "987007536441005171" |
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