Recently in a reading I was doing, I ran into a fact I do not seem to be able to prove.
The claim was that finite direct limits commute with inverse limits.
It was also claimed that inverse limits commute (without finiteness).
Under what conditions is this true? Is it true in any category with direct and inverse limits, or is some set like structure required for proof? Additionally, I would like to read a proof of the above mentioned statements if you would be willing either to answer with one or tell me where I could find one.
Thank you much for any help or direction.