 Sieve (category theory)

A sieve on $U$ is a subfunctor of the representable functor $yU$, 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 $fg$ belongs to the original sieve.

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.