Derived functor

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

\[ M\mapsto M^{G} \]

related items

• Ext functor
• Free resolutions

메타데이터

위키데이터

• ID : Q320245