Limits and colimits

Limits and colimits as adjoints to the diagonal

Let be categories with small, and consider the diagonal functor

from to its category of diagrams. Then the left and right adjoints of , if they exist are given by colimits and limits respectively.1

Proof

#missing/proof

#state/develop | #lang/en | #SemBr

Footnotes

  1. 2010. Category theory, §9.3, pp. 217–218. ↩