Kan Extensions

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On page 248 of Categories for the Working Mathematician[1], Saunders Mac Lane stated:

The notion of Kan extensions subsumes all the other fundamental concepts of category theory.

Kan Extensions are partial colimits

Paolo Perrone has a few talks on explaining Kan Extensions as partial colimits[2][3][4].

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References

  1. Mac Lane, Saunders (1998). Categories for the Working Mathematician. Graduate Texts in Mathematics. 5 (2nd ed.). local page: Springer-Verlag. ISBN 0-387-98403-8. Zbl 0906.18001.  , 248
  2. {{:Video/Kan extensions are partial colimits, Paolo Perrone, 11/02/2021
  3. Perrone, Paolo (Feb 28, 2022). Perrone - Kan extensions are partial colimits. local page: Category Theory CT20->21. 
  4. Perrone, Paolo (Jun 12, 2020). Paolo Perrone: Kan extensions are partial colimits. local page: Topos Institute.