Generally, in a category$\mathcal{C}$, one of the more usual forms of a filtered object encountered is an object$X$ equipped with a filtration. A descending filtration is a sequence of monomorphisms of the form

There are variants in which the sequence may be infinite ‘to the right’ or may be bounded or stationary in some way to the left. In situations where quotients make sense, extra conditions on the quotients $X_{(n)}/X_{(n+1)}$, are often imposed; see associated graded object.