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数学

Discovery

Andrius Kulikauskas

  • ms@ms.lt
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  • My work is in the Public Domain for all to share freely.

Lietuvių kalba

Introduction E9F5FC

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software


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.

LimitsVsColimits


Naujausi pakeitimai


Puslapis paskutinį kartą pakeistas 2019 vasario 12 d., 12:36
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