- Express and compare a center and a totality in terms of limits.
- Express choice frameworks in terms of limits.
Examples of limits
- inverse limits
- terminal objects
- equalizers, kernels
Examples of colimits
- coproducts, disjoint unions, direct sums, copowers
- direct limits
- initial objects
- coequalizers, cokernels
Differences between limits and colimits
- A cone has arrows from a limit to the objects in a diagram.
- A cocone has arrows from the objects in a diagram to a limit.
- Initial objects (such as the empty set) are the most primordial objects. They are the internal emptiness.
- Terminal objects (such as singletons) are the most degenerate objects. They are external trivialities, like points.
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.