Nicht lieferbar
Sieve (Category Theory)
Schade – dieser Artikel ist leider ausverkauft. Sobald wir wissen, ob und wann der Artikel wieder verfügbar ist, informieren wir Sie an dieser Stelle.
  • Broschiertes Buch

High Quality Content by WIKIPEDIA articles! In category theory, a branch of mathematics, a sieve is a way of choosing arrows with a common codomain. It is a categorical analogue of a collection of open subsets of a fixed open set in topology. In a Grothendieck topology, certain sieves become categorical analogues of open covers in topology. Let C be a category, and let c be an object of C. A sieve S on c is a subfunctor of Hom( , c), i.e., for all objects c of C, S(c ) Hom(c , c), and for all arrows f:c c , S(f) is the restriction of Hom(f, c), the pullback by f, to S(c ). Put another way, a…mehr

Andere Kunden interessierten sich auch für
Produktbeschreibung
High Quality Content by WIKIPEDIA articles! In category theory, a branch of mathematics, a sieve is a way of choosing arrows with a common codomain. It is a categorical analogue of a collection of open subsets of a fixed open set in topology. In a Grothendieck topology, certain sieves become categorical analogues of open covers in topology. Let C be a category, and let c be an object of C. A sieve S on c is a subfunctor of Hom( , c), i.e., for all objects c of C, S(c ) Hom(c , c), and for all arrows f:c c , S(f) is the restriction of Hom(f, c), the pullback by f, to S(c ). Put another way, a sieve is a collection S of arrows with a common codomain which satisfies the functoriality condition, "If g:c c is an arrow in S, and if f:c c is any other arrow in C, then the pullback gf of g by f is in S." Consequently sieves are similar to right ideals in ring theory or filters in order theory. The most common operation on a sieve is pullback. Pulling back a sieve S on c by an arrow f:c cgives a new sieve f S on c . This new sieve consists of all the arrows in S which factor through c .