# What's the meaning of “decreasing filtration”?

Page 152-153, "Algebraic Geometry" by Lei Fu.

The condition (e) of the definition of spectral sequence is listed as follows:

(e) A family of objects $H^n(n\in \Bbb Z)$ in $\mathcal C$ and each $H^n$ is provided with a decreasing filtration $$\cdots \supset F^pH^n \supset F^{p+1}H^n \supset\cdots.$$

What's the meaning of "decreasing filtration"?

It's explained in the line following the term. A sequence of indexed objects (I'd assume subsets of $H^n$ in this case) with the inclusion relation "$\supset$". The word decreasing refers to the direction of the inclusion. (If you'd replace "$\supset$" by "$\subset$" it would be increasing. )
(Sometimes additional requirements are imposed, e.g. that $H^n$ is the limit (in whatever sense) of the sequence in the increasing direction or $\{0\}$ the limit in the other direction, but I'd expect this to be stated).