Whenever editing is allowed on the nLab again, this article should be ported over there.
A net is a function from a directed type to a type . is called the index type, the terms of are called indices (singular index), and is called the indexed type.
Let be a type, let be a directed type, and let be a net. Given a term , the positive cone of with respect to is defined as the type
with monic function such that for all terms , .
Given a subtype of with monic function , is eventually in if comes with a term and a function such that for all terms , .