Filtration (mathematics)
In mathematics, a filtration F {\displaystyle {\mathcal {F}}} is, informally, like a set of ever larger Russian dolls, each one containing the previous ones, where a "doll" is a subobject of an algebraic structure. Formally, a filtration is an indexed family ( S i ) i ∈ I {\displaystyle (S_{i})_{i\in I}} of subobjects of a given algebraic structure S {\displaystyle S} , with the index i {\displaystyle i} running over some totally ordered index set I {\displaystyle I} , subject to the condition that if i ≤ j {\displaystyle i\leq j} in I {\displaystyle I} , then S i ⊆ S j {\displaystyle S_{i}\subseteq S_{j}} .