Sieve

A sieve, or sifter, is a device for separating wanted elements from unwanted material or for characterizing the particle size distribution of a sample, typically using a woven screen such as a mesh or net or metal. The word "sift" derives from "sieve". In cooking, a sifter is used to separate and break up clumps in dry ingredients such as flour, as well as to aerate and combine them. A strainer is a form of sieve used to separate solids from liquid.

Industrial strainer

Some industrial strainers available are simplex basket strainers, duplex basket strainers, and Y strainers. Simple basket strainers are used to protect valuable or sensitive equipment in systems that are meant to be shut down temporarily. Some commonly used strainers are bell mouth strainers, foot valve strainers, basket strainers. Most processing industries (mainly pharmaceutical, coatings and liquid food industries) will opt for a self-cleaning strainer instead of a basket strainer or a simplex strainer due to limitations of simple filtration systems. The self-cleaning strainers or filters are more efficient and provide an automatic filtration solution.

Sieve (mail filtering language)

Sieve is a programming language that can be used for email filtering. It owes its creation to the CMU Cyrus Project, creators of Cyrus IMAP server.

The language is not tied to any particular operating system or mail architecture. It requires the use of RFC 2822-compliant messages, but otherwise should generalize to other systems that meet these criteria. The current version of Sieve's base specification is outlined in RFC 5228, published in January 2008.

Language

Sieve is a data-driven programming language, similar to earlier email filtering languages such as procmail and maildrop, and earlier line-oriented languages such as sed and AWK: it specifies conditions to match and actions to take on matching.

This differs from general-purpose programming languages in that it is highly limited – the base standard has no variables, and no loops (but does allowing conditional branching), preventing runaway programs and limiting the language to simple filtering operations. Although extensions have been devised to extend the language to include variables and, to a limited degree, loops, the language is still highly restricted, and thus unsuitable for running user-devised programs as part of the mail system.

Sieve (category theory)

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.

Definition

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 (in the sense of precomposition, not of fiber products), 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 S(f)(g) = gf is in S." Consequently sieves are similar to right ideals in ring theory or filters in order theory.

Pullback of sieves

The most common operation on a sieve is pullback. Pulling back a sieve S on c by an arrow f:c′→c gives a new sieve f^*S on c′. This new sieve consists of all the arrows in S which factor through c′.