Investigation: Explore how limits describe external relations whereas colimits describe internal structure.
Examples of limits
Examples of colimits
Differences between limits and colimits
Moving from internal structure to external representations - from How to What. And then we also move from the sum of external relations (why) to the inherent internal reference (Whether). So this is a (one-sided?) dual direction.
Concept of limits. Terrence Tao: Analytic limits need neighborhoods. Categorical limits need maps. Third kind of limit: Ultraproducts.