# Inverse Image

### Some articles on inverse image, image, images:

Exceptional Inverse Image Functor - 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 map of ... Then the exceptional inverse image is a functor Rf! D(Y) → D(X) where D(–) denotes the derived category of sheaves of abelian groups or modules over a fixed ring ... be the right adjoint of the total derived functor Rf! of the direct image with compact support ...
Image Functors For Sheaves
... as topology, logic and algebraic geometry, there are four image functors for sheaves which belong together in various senses ... The functors in question are direct image f∗ Sh(X) → Sh(Y) inverse image f∗ Sh(Y) → Sh(X) direct image with compact support f! Sh(X) → Sh(Y) exceptional inverse image Rf! D(Sh(Y)) → D(Sh(X)) ... The exceptional inverse image is in general defined on the level of derived categories only ...
Coherent Duality - Adjoint Functor Point of View
... Image functors for sheaves direct image f∗ inverse image f∗ direct image with compact support f! exceptional inverse image Rf! While Serre duality uses a line bundle or invertible sheaf as a dualizing sheaf ... as the existence of a right adjoint functor f !, called twisted or exceptional inverse image functor, to a higher direct image with compact support functor Rf! ... Higher direct images are a sheafified form of sheaf cohomology in this case with proper (compact) support they are bundled up into a single functor by means of the derived category formulation of homological ...

### Famous quotes containing the words image and/or inverse:

True revolutionaries are like God—they create the world in their own image. Our awesome responsibility to ourselves, to our children, and to the future is to create ourselves in the image of goodness, because the future depends on the nobility of our imaginings.
Barbara Grizzuti Harrison (b. 1941)

The quality of moral behaviour varies in inverse ratio to the number of human beings involved.
Aldous Huxley (1894–1963)