Sir, yes sir.

to stake out a new road

An inverse limit has “natural projections” which are restrictions of the projections of the Cartesian product (to a domain which is the inverse limit). The reason why the projections are described as “natural” would be the following: besides the functor from an index poset to the inverse system, there is another functor from the same index poset to the inverse limit of that system, this functor being a constant functor. Then there is a natural transformation from the constant functor to the inverse limit’s functor: the components of such natural transformation are the said “natural projections”.

The sell side exists only because the buy side trades before we can understand when the sell side is profitable.