Presheaf

/ˈpriːʃiːf/

/ˈpriːʃif/

Translation of "presheaf" into Russian

Noun

/ˈpriːʃiːf/

/ˈpriːʃif/

presheaf

presheaves pl

предпучок

A presheaf is a functor that assigns data to open sets of a topological space.

Предпучок — это функтор, который присваивает данные открытым множествам топологического пространства.

Noun

/ˈpriːʃiːf/

/ˈpriːʃif/

A mathematical structure in category theory that assigns data to open sets of a topological space and satisfies certain consistency conditions.

In algebraic geometry, a presheaf can be used to assign a ring of functions to each open set of a variety.

More generally, any contravariant functor F: C^{op} → Set, regarded abstractly as a presheaf on the category C.

Viewed abstractly, every small category C admits a category of presheaves on C.

Adjective

/ˈpriːʃiːf/

/ˈpriːʃif/

Relating to or characteristic of a presheaf.

The presheaf construction is fundamental in topos theory.