Ind- and pro-objects, reference request

Question

Can someone point me to a good exposition of ind- and pro-objects, the intuition behind, and how one "in practice" works with them (i.e. prove things)? The nlab page is nice (especially for the intuition) but not very introductory, and I cannot seem to find any other "official" page about them.

Answer 1

There are mainly two sources of motivation for the definition of ind- and pro-object:

1. Certain pieces of algebraic geometry and algebraic analysis, a good introduction to which is the book "Ind-sheaves"(click);
2. Certain pieces of categorically-minded Algebraic Topology, especially the short book "Categorical Constructions in Stable Homotopy Theory" who taught me the essence of the construction of the category of spectra: (click)

Hope it helps!