Turning A Presheaf Into A Sheaf
It is frequently useful to take the data contained in a presheaf and to express it as a sheaf. It turns out that there is a best possible way to do this. It takes a presheaf F and produces a new sheaf aF called the sheaving, sheafification or sheaf associated to the presheaf F. a is called the sheaving functor, sheafification functor, or associated sheaf functor. There is a natural morphism of presheaves i : F → aF that has the universal property that for any sheaf G and any morphism of presheaves f : F → G, there is a unique morphism of sheaves such that . In fact a is the adjoint functor to the inclusion functor from the category of sheaves to the category of presheaves, and i is the unit of the adjunction.
Read more about this topic: Sheaf (mathematics)
Famous quotes containing the words turning a and/or turning:
“The white American man makes the white American woman maybe not superfluous but just a little kind of decoration. Not really important to turning around the wheels of the state. Well the black American woman has never been able to feel that way. No black American man at any time in our history in the United States has been able to feel that he didn’t need that black woman right against him, shoulder to shoulder—in that cotton field, on the auction block, in the ghetto, wherever.”
—Maya Angelou (b. 1928)
“The function of comedy is to dispel ... unconsciousness by turning the searchlight of the keenest moral and intellectual analysis right on to it.”
—George Bernard Shaw (1856–1950)