Definition
| Image functors for sheaves |
|---|
| direct image f∗ |
| inverse image f∗ |
| direct image with compact support f! |
| exceptional inverse image Rf! |
Let f: X → Y be a continuous mapping of topological spaces, and Sh(–) the category of sheaves of abelian groups on a topological space. The direct image functor
sends a sheaf F on X to its direct image presheaf
which turns out be a sheaf on Y. This assignment is functorial, i.e. a morphism of sheaves φ: F → G on X gives rise to a morphism of sheaves f∗(φ): f∗(F) → f∗(G) on Y.
Read more about this topic: Direct Image Functor
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