"Derived functor"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
imported>Pythagoras0 (새 문서: ==introduction== * basic tool to define cohomology theory * extend a left invariant functor to get a derived functor * then we get a cohomology theory * e.g. sheaf cohomology of a top...) |
Pythagoras0 (토론 | 기여) |
||
| (사용자 2명의 중간 판 4개는 보이지 않습니다) | |||
| 3번째 줄: | 3번째 줄: | ||
* extend a left invariant functor to get a derived functor | * extend a left invariant functor to get a derived functor | ||
* then we get a cohomology theory | * then we get a cohomology theory | ||
| − | * e.g. sheaf cohomology of a topological space X with coefficients in a sheaf | + | * e.g. sheaf cohomology of a topological space X with coefficients in a sheaf <math>\mathcal F</math> = the right derived functor of the global section functor |
==left invariant functors== | ==left invariant functors== | ||
===global section functor=== | ===global section functor=== | ||
| − | * a functor from sheaves on | + | * a functor from sheaves on <math>X</math> to abelian groups defined by |
| − | + | :<math> | |
\mathcal F \mapsto H^{0}(X, \mathcal F) | \mathcal F \mapsto H^{0}(X, \mathcal F) | ||
| − | + | </math> | |
===invariants=== | ===invariants=== | ||
| − | * | + | * <math>G</math> : group |
| − | * from modules of | + | * from modules of <math>G</math> to abelian groups |
| − | + | :<math> | |
M\mapsto M^{G} | M\mapsto M^{G} | ||
| − | + | </math> | |
| + | |||
| + | |||
| + | ==related items== | ||
| + | * [[Ext functor]] | ||
| + | * [[Free resolutions]] | ||
| + | |||
[[분류:Abstract concepts]] | [[분류:Abstract concepts]] | ||
| + | [[분류:migrate]] | ||
| + | |||
| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q320245 Q320245] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'derived'}, {'LEMMA': 'functor'}] | ||
2021년 2월 17일 (수) 01:36 기준 최신판
introduction
- basic tool to define cohomology theory
- extend a left invariant functor to get a derived functor
- then we get a cohomology theory
- e.g. sheaf cohomology of a topological space X with coefficients in a sheaf \(\mathcal F\) = the right derived functor of the global section functor
left invariant functors
global section functor
- a functor from sheaves on \(X\) to abelian groups defined by
\[ \mathcal F \mapsto H^{0}(X, \mathcal F) \]
invariants
- \(G\) : group
- from modules of \(G\) to abelian groups
\[ M\mapsto M^{G} \]
메타데이터
위키데이터
- ID : Q320245
Spacy 패턴 목록
- [{'LOWER': 'derived'}, {'LEMMA': 'functor'}]