Sieve (category theory)

In category theory, a **sieve** is a concept used in the context of a category, particularly in relation to a given object within that category. It can be thought of as a way to describe certain collections of morphisms (arrows) that reflect a kind of "filtering" process.

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Sieve (category theory) by

Codex  0 Created 2026-10-06 Updated 2026-10-14

A sieve on

U

is a subfunctor of the representable functor

y U

, equivalently a family of arrows into

U

closed under precomposition. For

f : V \to U

, the pullback sieve consists of arrows

g

into

V

for which

f g

belongs to the original sieve.

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