See: Math notebook, Category theory, Category theory glossary

**Investigation: Explore how limits describe external relations whereas colimits describe internal structure.**

- Express and compare a center and a totality in terms of limits.
- Express choice frameworks in terms of limits.

**Readings**

Examples of limits

- products
- pullbacks
- inverse limits
- terminal objects
- equalizers, kernels

Examples of colimits

- coproducts, disjoint unions, direct sums, copowers
- pushouts
- 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.

Concept of limits. Terrence Tao: Analytic limits need neighborhoods. Categorical limits need maps. Third kind of limit: Ultraproducts.

Parsiųstas iš http://www.ms.lt/sodas/Book/LimitsVsColimits

Puslapis paskutinį kartą pakeistas 2020 balandžio 13 d., 14:09